[d694de] | 1 | //GMG, last modified 18.6.99 |
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[ebbe4a] | 2 | //anne, added deleteSublist and watchdog 12.12.2000 |
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[ca41246] | 3 | //eric, added absValue 11.04.2002 |
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[3d124a7] | 4 | /////////////////////////////////////////////////////////////////////////////// |
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[341696] | 5 | version="$Id$"; |
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[49998f] | 6 | category="General purpose"; |
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[5480da] | 7 | info=" |
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[803c5a1] | 8 | LIBRARY: general.lib Elementary Computations of General Type |
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[3d124a7] | 9 | |
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[f34c37c] | 10 | PROCEDURES: |
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[0b59f5] | 11 | A_Z(\"a\",n); string a,b,... of n comma separated letters |
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[63be42] | 12 | ASCII([n,m]); string of printable ASCII characters (number n to m) |
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[ca41246] | 13 | absValue(c); absolute value of c |
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[fc62b67] | 14 | binomial(n,m[,../..]); n choose m (type int), [type bigint] |
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[ebbe4a] | 15 | deleteSublist(iv,l); delete entries given by iv from list l |
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[fc62b67] | 16 | factorial(n[,../..]); n factorial (=n!) (type int), [type bigint] |
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[3d124a7] | 17 | fibonacci(n[,p]); nth Fibonacci number [char p] |
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[dd2aa36] | 18 | kmemory([n[,v]]); active [allocated] memory in kilobyte |
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[3d124a7] | 19 | killall(); kill all user-defined variables |
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| 20 | number_e(n); compute exp(1) up to n decimal digits |
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| 21 | number_pi(n); compute pi (area of unit circle) up to n digits |
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| 22 | primes(n,m); intvec of primes p, n<=p<=m |
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| 23 | product(../..[,v]); multiply components of vector/ideal/...[indices v] |
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| 24 | sort(ideal/module); sort generators according to monomial ordering |
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| 25 | sum(vector/id/..[,v]); add components of vector/ideal/...[with indices v] |
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[ebbe4a] | 26 | watchdog(i,cmd); only wait for result of command cmd for i seconds |
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[63be42] | 27 | which(command); search for command and return absolute path, if found |
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[298d0a] | 28 | primecoeffs(J[,q]); primefactors <= min(p,32003) of coeffs of J |
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[90d772] | 29 | timeStd(i,d) std(i) if the standard basis computation finished |
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| 30 | after d-1 seconds and i otherwhise |
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| 31 | timeFactorize(p,d) factorize(p) if the factorization finished after d-1 |
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| 32 | seconds otherwhise f is considered to be irreducible |
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| 33 | factorH(p) changes variables to become the last variable the |
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| 34 | principal one in the multivariate factorization and |
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| 35 | factorizes then the polynomial |
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| 36 | |
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[194f5e5] | 37 | (parameters in square brackets [] are optional) |
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[5480da] | 38 | "; |
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| 39 | |
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[3d124a7] | 40 | LIB "inout.lib"; |
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[8b87364] | 41 | LIB "poly.lib"; |
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| 42 | LIB "matrix.lib"; |
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[3d124a7] | 43 | /////////////////////////////////////////////////////////////////////////////// |
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| 44 | |
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| 45 | proc A_Z (string s,int n) |
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[d2b2a7] | 46 | "USAGE: A_Z(\"a\",n); a any letter, n integer (-26<= n <=26, !=0) |
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[3d124a7] | 47 | RETURN: string of n small (if a is small) or capital (if a is capital) |
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[0b59f5] | 48 | letters, comma separated, beginning with a, in alphabetical |
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[a7a00b] | 49 | order (or reverse alphabetical order if n<0) |
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[3d124a7] | 50 | EXAMPLE: example A_Z; shows an example |
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[d2b2a7] | 51 | " |
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[3d124a7] | 52 | { |
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| 53 | if ( n>=-26 and n<=26 and n!=0 ) |
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| 54 | { |
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| 55 | string alpha = |
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| 56 | "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,"+ |
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| 57 | "a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,"+ |
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| 58 | "A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,"+ |
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| 59 | "A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z"; |
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| 60 | int ii; int aa; |
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| 61 | for(ii=1; ii<=51; ii=ii+2) |
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| 62 | { |
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| 63 | if( alpha[ii]==s ) { aa=ii; } |
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| 64 | } |
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| 65 | if ( aa==0) |
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| 66 | { |
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| 67 | for(ii=105; ii<=155; ii=ii+2) |
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| 68 | { |
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| 69 | if( alpha[ii]==s ) { aa=ii; } |
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| 70 | } |
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| 71 | } |
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| 72 | if( aa!=0 ) |
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| 73 | { |
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| 74 | string out; |
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| 75 | if (n > 0) { out = alpha[aa,2*(n)-1]; return (out); } |
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| 76 | if (n < 0) |
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| 77 | { |
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| 78 | string beta = |
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| 79 | "z,y,x,w,v,u,t,s,r,q,p,o,n,m,l,k,j,i,h,g,f,e,d,c,b,a,"+ |
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| 80 | "z,y,x,w,v,u,t,s,r,q,p,o,n,m,l,k,j,i,h,g,f,e,d,c,b,a,"+ |
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| 81 | "Z,Y,X,W,V,U,T,S,R,Q,P,O,N,M,L,K,J,I,H,G,F,E,D,C,B,A,"+ |
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| 82 | "Z,Y,X,W,V,U,T,S,R,Q,P,O,N,M,L,K,J,I,H,G,F,E,D,C,B,A"; |
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| 83 | if ( aa < 52 ) { aa=52-aa; } |
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| 84 | if ( aa > 104 ) { aa=260-aa; } |
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| 85 | out = beta[aa,2*(-n)-1]; return (out); |
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| 86 | } |
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| 87 | } |
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| 88 | } |
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| 89 | } |
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| 90 | example |
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| 91 | { "EXAMPLE:"; echo = 2; |
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| 92 | A_Z("c",5); |
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| 93 | A_Z("Z",-5); |
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| 94 | string sR = "ring R = (0,"+A_Z("A",6)+"),("+A_Z("a",10)+"),dp;"; |
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| 95 | sR; |
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[034ce1] | 96 | execute(sR); |
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[3d124a7] | 97 | R; |
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| 98 | } |
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| 99 | /////////////////////////////////////////////////////////////////////////////// |
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[63be42] | 100 | proc ASCII (list #) |
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| 101 | "USAGE: ASCII([n,m]); n,m= integers (32 <= n <= m <= 126) |
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[a7a00b] | 102 | RETURN: string of printable ASCII characters (no native language support)@* |
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| 103 | ASCII(): string of all ASCII characters with its numbers,@* |
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| 104 | ASCII(n): n-th ASCII character@* |
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[b42ab6] | 105 | ASCII(n,m): n-th up to m-th ASCII character (inclusive) |
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[63be42] | 106 | EXAMPLE: example ASCII; shows an example |
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| 107 | " |
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| 108 | { |
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| 109 | string s1 = |
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[008846] | 110 | " ! \" # $ % & ' ( ) * + , - . |
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[63be42] | 111 | 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 |
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| 112 | / 0 1 2 3 4 5 6 7 8 9 : ; < = |
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| 113 | 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 |
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| 114 | > ? @ A B C D E F G H I J K L |
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| 115 | 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 |
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| 116 | M N O P Q R S T U V W X Y Z [ |
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| 117 | 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 |
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| 118 | \\ ] ^ _ ` a b c d e f g h i j |
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| 119 | 92 93 94 95 96 97 98 99 100 101 102 103 104 105 10 |
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| 120 | k l m n o p q r s t u v w x y |
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| 121 | 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 |
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| 122 | z { | } ~ |
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| 123 | 122 123 124 125 126 "; |
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| 124 | |
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| 125 | string s2 = |
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| 126 | " !\"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~"; |
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| 127 | |
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| 128 | if ( size(#) == 0 ) |
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| 129 | { |
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| 130 | return(s1); |
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| 131 | } |
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| 132 | if ( size(#) == 1 ) |
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| 133 | { |
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| 134 | return( s2[#[1]-31] ); |
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| 135 | } |
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| 136 | if ( size(#) == 2 ) |
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| 137 | { |
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| 138 | return( s2[#[1]-31,#[2]-#[1]+1] ); |
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| 139 | } |
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| 140 | } |
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| 141 | example |
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| 142 | { "EXAMPLE:"; echo = 2; |
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| 143 | ASCII();""; |
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| 144 | ASCII(42); |
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| 145 | ASCII(32,126); |
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| 146 | } |
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| 147 | /////////////////////////////////////////////////////////////////////////////// |
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[3d124a7] | 148 | |
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[ca41246] | 149 | proc absValue(def c) |
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[298d0a] | 150 | "USAGE: absValue(c); c int, number or poly |
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[ca41246] | 151 | RETURN: absValue(c); the absolute value of c |
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| 152 | NOTE: absValue(c)=c if c>=0; absValue=-c if c<=0. |
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| 153 | @* So the function can be applied to any type, for which comparison |
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[298d0a] | 154 | @* operators are defined. |
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[ca41246] | 155 | EXAMPLE: example absValue; shows an example |
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| 156 | " |
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| 157 | { |
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| 158 | if (c>=0) { return(c); } |
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| 159 | else { return(-c); } |
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| 160 | } |
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| 161 | example |
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| 162 | { "EXAMPLE:"; echo = 2; |
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| 163 | ring r1 = 0,x,dp; |
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| 164 | absValue(-2002); |
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| 165 | |
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| 166 | poly f=-4; |
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| 167 | absValue(f); |
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| 168 | } |
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| 169 | /////////////////////////////////////////////////////////////////////////////// |
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| 170 | |
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[fc62b67] | 171 | proc binomial (int n, int k) |
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| 172 | "USAGE: binomial(n,k); n,k integers |
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[b42ab6] | 173 | RETURN: binomial(n,k); binomial coefficient n choose k |
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[fc62b67] | 174 | @* - of type bigint (computed in characteristic 0) |
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[c860e9] | 175 | NOTE: In any characteristic, binomial(n,k) = coefficient of x^k in (1+x)^n |
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[b42ab6] | 176 | SEE ALSO: prime |
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[3d124a7] | 177 | EXAMPLE: example binomial; shows an example |
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[d2b2a7] | 178 | " |
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[3d124a7] | 179 | { |
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[fc62b67] | 180 | bigint l; |
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| 181 | bigint r=1; |
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| 182 | bigint kk=k; |
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| 183 | bigint nn=n; |
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| 184 | if ( k > n-k ) |
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| 185 | { k = n-k; } |
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| 186 | if ( k<=0 or k>n ) //trivial cases |
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| 187 | { r = (k==0)*r; } |
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| 188 | for (l=1; l<=kk; l=l+1 ) |
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[c860e9] | 189 | { |
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[fc62b67] | 190 | r=r*(nn+1-l)/l; |
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[c860e9] | 191 | } |
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[fc62b67] | 192 | return(r); |
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| 193 | } |
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[3d124a7] | 194 | example |
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| 195 | { "EXAMPLE:"; echo = 2; |
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[883957] | 196 | binomial(200,100);""; //type bigint |
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[c860e9] | 197 | int n,k = 200,100; |
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[7f3ad4] | 198 | bigint b1 = binomial(n,k); |
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[c860e9] | 199 | ring r = 0,x,dp; |
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[883957] | 200 | poly b2 = coeffs((x+1)^n,x)[k+1,1]; //coefficient of x^k in (x+1)^n |
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| 201 | b1-b2; //b1 and b2 should coincide |
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[c860e9] | 202 | } |
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| 203 | /////////////////////////////////////////////////////////////////////////////// |
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| 204 | |
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| 205 | static proc binomp (int n, int k, int p) |
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| 206 | //computes binomial coefficient n choose k in basering of char p > 0 |
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| 207 | //binomial(n,k) = coefficient of x^k in (1+x)^n. |
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| 208 | //Let n=q*p^j, gcd(q,p)=1, then (1+x)^n = (1 + x^(p^j))^q. We have |
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| 209 | //binomial(n,k)=0 if k!=l*p^j and binomial(n,l*p^j) = binomial(q,l). |
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| 210 | //Do this reduction first. Then, in denominator and numerator |
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| 211 | //of defining formula for binomial coefficient, reduce those factors |
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| 212 | //mod p which are not divisible by p and cancel common factors p. Hence, |
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| 213 | //if n = h*p+r, k=l*p+s, r,s<p, binomial(n,k) = binomial(r,s)*binomial(h,l) |
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| 214 | { |
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| 215 | int l,q,i= 1,n,1; |
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| 216 | number r=1; |
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| 217 | if ( k > n-k ) |
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| 218 | { k = n-k; |
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| 219 | } |
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| 220 | if ( k<=0 or k>n) //trivial cases |
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| 221 | { r = (k==0)*r; |
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| 222 | } |
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| 223 | else |
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| 224 | { |
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| 225 | while ( q mod p == 0 ) |
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| 226 | { l = l*p; |
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| 227 | q = q div p; |
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| 228 | } //we have now n=q*l, l=p^j, gcd(q,p)=1; |
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| 229 | if (k mod l != 0 ) |
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| 230 | { r = 0; |
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| 231 | } |
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| 232 | else |
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| 233 | { l = k div l; |
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| 234 | n = q mod p; |
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| 235 | k = l mod p; //now 0<= k,n <p, use binom0 for n,k |
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| 236 | q = q div p; //recursion for q,l |
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| 237 | l = l div p; //use binomp for q,l |
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| 238 | r = binom0(n,k)*binomp(q,l,p); |
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| 239 | } |
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| 240 | } |
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| 241 | return(r); |
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[3d124a7] | 242 | } |
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| 243 | /////////////////////////////////////////////////////////////////////////////// |
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| 244 | |
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[fc62b67] | 245 | proc factorial (int n) |
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| 246 | "USAGE: factorial(n); n integer |
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| 247 | RETURN: factorial(n): n! of type bigint. |
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[b42ab6] | 248 | SEE ALSO: prime |
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| 249 | EXAMPLE: example factorial; shows an example |
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[d2b2a7] | 250 | " |
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[fc62b67] | 251 | { |
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| 252 | bigint r=1; |
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[c860e9] | 253 | //------------------------------ computation -------------------------------- |
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[a292211] | 254 | for (int l=2; l<=n; l++) |
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[3d124a7] | 255 | { |
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[f937e2] | 256 | r=r*l; |
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[3d124a7] | 257 | } |
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[fc62b67] | 258 | return(r); |
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[3d124a7] | 259 | } |
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| 260 | example |
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| 261 | { "EXAMPLE:"; echo = 2; |
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[fc62b67] | 262 | factorial(37);""; //37! (as long integer) |
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[3d124a7] | 263 | } |
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| 264 | /////////////////////////////////////////////////////////////////////////////// |
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| 265 | |
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[fc62b67] | 266 | proc fibonacci (int n) |
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| 267 | "USAGE: fibonacci(n); n,p integers |
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[b42ab6] | 268 | RETURN: fibonacci(n): nth Fibonacci number, f(0)=f(1)=1, f(i+1)=f(i-1)+f(i) |
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[fc62b67] | 269 | @* - computed in characteristic 0, of type bigint |
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[b42ab6] | 270 | SEE ALSO: prime |
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[3d124a7] | 271 | EXAMPLE: example fibonacci; shows an example |
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[d2b2a7] | 272 | " |
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[fc62b67] | 273 | { |
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| 274 | bigint f,g,h=1,1,1; |
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[c860e9] | 275 | //------------------------------ computation -------------------------------- |
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[f937e2] | 276 | for (ii=3; ii<=n; ii=ii+1) |
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[3d124a7] | 277 | { |
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[f937e2] | 278 | h = f+g; f = g; g = h; |
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[fc62b67] | 279 | } |
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| 280 | return(h); |
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[3d124a7] | 281 | } |
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| 282 | example |
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| 283 | { "EXAMPLE:"; echo = 2; |
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[b42ab6] | 284 | fibonacci(42); ""; //f(42) of type string (as long integer) |
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| 285 | ring r = 2,x,dp; |
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| 286 | number b = fibonacci(42,2); //f(42) of type number, computed in r |
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[c860e9] | 287 | b; |
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[3d124a7] | 288 | } |
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| 289 | /////////////////////////////////////////////////////////////////////////////// |
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| 290 | |
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[d694de] | 291 | proc kmemory (list #) |
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[b42ab6] | 292 | "USAGE: kmemory([n,[v]]); n,v integers |
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[a7a00b] | 293 | RETURN: memory in kilobyte of type bigint |
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[b42ab6] | 294 | @* n=0: memory used by active variables (same as no parameters) |
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| 295 | @* n=1: total memory allocated by Singular |
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[dd2aa36] | 296 | DISPLAY: detailed information about allocated and used memory if v!=0 |
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[d694de] | 297 | NOTE: kmemory uses internal function 'memory' to compute kilobyte, and |
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| 298 | is the same as 'memory' for n!=0,1,2 |
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[3d124a7] | 299 | EXAMPLE: example kmemory; shows an example |
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[d2b2a7] | 300 | " |
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[917fb5] | 301 | { |
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[d694de] | 302 | int n; |
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[dd2aa36] | 303 | int verb; |
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[d694de] | 304 | if (size(#) != 0) |
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| 305 | { |
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| 306 | n=#[1]; |
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[dd2aa36] | 307 | if (size(#) >1) |
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| 308 | { verb=#[2]; } |
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[d694de] | 309 | } |
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[917fb5] | 310 | |
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[dd2aa36] | 311 | if ( verb != 0) |
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| 312 | { |
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| 313 | if ( n==0) |
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| 314 | { dbprint(printlevel-voice+3, |
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| 315 | "// memory used, at the moment, by active variables (kilobyte):"); } |
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| 316 | if ( n==1 ) |
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| 317 | { dbprint(printlevel-voice+3, |
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| 318 | "// total memory allocated, at the moment, by SINGULAR (kilobyte):"); } |
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[c60d60] | 319 | } |
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| 320 | return ((memory(n)+1023) div 1024); |
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[3d124a7] | 321 | } |
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| 322 | example |
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| 323 | { "EXAMPLE:"; echo = 2; |
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| 324 | kmemory(); |
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[dd2aa36] | 325 | kmemory(1,1); |
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[3d124a7] | 326 | } |
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| 327 | /////////////////////////////////////////////////////////////////////////////// |
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| 328 | |
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| 329 | proc killall |
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[d2b2a7] | 330 | "USAGE: killall(); (no parameter) |
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| 331 | killall(\"type_name\"); |
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| 332 | killall(\"not\", \"type_name\"); |
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[b42ab6] | 333 | RETURN: killall(); kills all user-defined variables except loaded procedures, |
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| 334 | no return value. |
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| 335 | @* - killall(\"type_name\"); kills all user-defined variables, |
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| 336 | of type \"type_name\" |
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| 337 | @* - killall(\"not\", \"type_name\"); kills all user-defined variables, |
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| 338 | except those of type \"type_name\" and except loaded procedures |
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[65546eb] | 339 | @* - killall(\"not\", \"name_1\", \"name_2\", ...); |
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| 340 | kills all user-defined variables, except those of name \"name_i\" |
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[b42ab6] | 341 | and except loaded procedures |
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[3d124a7] | 342 | NOTE: killall should never be used inside a procedure |
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| 343 | EXAMPLE: example killall; shows an example AND KILLS ALL YOUR VARIABLES |
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[d2b2a7] | 344 | " |
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[3d124a7] | 345 | { |
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[01cda73] | 346 | list @marie=names(Top); |
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[09f420] | 347 | int j, no_kill, @joni; |
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[b42ab6] | 348 | for ( @joni=1; @joni<=size(#); @joni++) |
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[5c187b] | 349 | { |
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[b42ab6] | 350 | if (typeof(#[@joni]) != "string") |
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[5c187b] | 351 | { |
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[b42ab6] | 352 | ERROR("Need string as " + string(@joni) + "th argument"); |
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[5c187b] | 353 | } |
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| 354 | } |
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[65546eb] | 355 | |
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[5c187b] | 356 | // kills all user-defined variables but not loaded procedures |
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| 357 | if( size(#)==0 ) |
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| 358 | { |
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[b42ab6] | 359 | for ( @joni=size(@marie); @joni>0; @joni-- ) |
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[5c187b] | 360 | { |
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[48c165a] | 361 | if( @marie[@joni]!="LIB" and typeof(`@marie[@joni]`)!="proc" |
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| 362 | and typeof(`@marie[@joni]`)!="package") |
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[b42ab6] | 363 | { kill `@marie[@joni]`; } |
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[5c187b] | 364 | } |
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| 365 | } |
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| 366 | else |
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| 367 | { |
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| 368 | // kills all user-defined variables |
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| 369 | if( size(#)==1 ) |
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| 370 | { |
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| 371 | // of type proc |
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| 372 | if( #[1] == "proc" ) |
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[3d124a7] | 373 | { |
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[b42ab6] | 374 | for ( @joni=size(@marie); @joni>0; @joni-- ) |
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[5c187b] | 375 | { |
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[298d0a] | 376 | if( (@marie[@joni]!="General") |
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[48c165a] | 377 | and (@marie[@joni]!="Top") |
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| 378 | and (@marie[@joni]!="killall") |
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[298d0a] | 379 | and (@marie[@joni]!="LIB") and |
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| 380 | ((typeof(`@marie[@joni]`)=="package") or |
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| 381 | (typeof(`@marie[@joni]`)=="proc"))) |
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| 382 | { |
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| 383 | if (defined(`@marie[@joni]`)) {kill `@marie[@joni]`;} |
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| 384 | } |
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| 385 | if (!defined(@joni)) break; |
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[48c165a] | 386 | } |
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[01cda73] | 387 | if (defined(General)) |
---|
[48c165a] | 388 | { |
---|
| 389 | @marie=names(General); |
---|
| 390 | for ( @joni=size(@marie); @joni>0; @joni-- ) |
---|
| 391 | { |
---|
| 392 | if(@marie[@joni]!="killall" |
---|
| 393 | and typeof(`@marie[@joni]`)=="proc") |
---|
| 394 | { kill General::`@marie[@joni]`; } |
---|
| 395 | } |
---|
| 396 | kill General::killall; |
---|
[5c187b] | 397 | } |
---|
[3d124a7] | 398 | } |
---|
[5c187b] | 399 | else |
---|
[65546eb] | 400 | { |
---|
[5c187b] | 401 | // other types |
---|
[b42ab6] | 402 | for ( @joni=size(@marie); @joni>2; @joni-- ) |
---|
[5c187b] | 403 | { |
---|
[65546eb] | 404 | if(typeof(`@marie[@joni]`)==#[1] and @marie[@joni]!="LIB" |
---|
| 405 | and typeof(`@marie[@joni]`)!="proc") |
---|
[b42ab6] | 406 | { kill `@marie[@joni]`; } |
---|
[5c187b] | 407 | } |
---|
| 408 | } |
---|
| 409 | } |
---|
| 410 | else |
---|
| 411 | { |
---|
[65546eb] | 412 | // kills all user-defined variables whose name or type is not #i |
---|
[b42ab6] | 413 | for ( @joni=size(@marie); @joni>2; @joni-- ) |
---|
[5c187b] | 414 | { |
---|
[a1b1dd] | 415 | if ( @marie[@joni] != "LIB" && @marie[@joni] != "Top" |
---|
| 416 | && typeof(`@marie[@joni]`) != "proc") |
---|
[5c187b] | 417 | { |
---|
| 418 | no_kill = 0; |
---|
[09f420] | 419 | for (j=2; j<= size(#); j++) |
---|
[6f2edc] | 420 | { |
---|
[b42ab6] | 421 | if (typeof(`@marie[@joni]`)==#[j] or @marie[@joni] == #[j]) |
---|
[5c187b] | 422 | { |
---|
| 423 | no_kill = 1; |
---|
| 424 | break; |
---|
| 425 | } |
---|
[6f2edc] | 426 | } |
---|
[5c187b] | 427 | if (! no_kill) |
---|
[6f2edc] | 428 | { |
---|
[b42ab6] | 429 | kill `@marie[@joni]`; |
---|
[6f2edc] | 430 | } |
---|
| 431 | } |
---|
[298d0a] | 432 | if (!defined(@joni)) break; |
---|
[5c187b] | 433 | } |
---|
| 434 | } |
---|
[6f2edc] | 435 | } |
---|
[3d124a7] | 436 | } |
---|
| 437 | example |
---|
| 438 | { "EXAMPLE:"; echo = 2; |
---|
[c860e9] | 439 | ring rtest; ideal i=x,y,z; string str="hi"; int j = 3; |
---|
| 440 | export rtest,i,str,j; //this makes the local variables global |
---|
| 441 | listvar(); |
---|
| 442 | killall("ring"); // kills all rings |
---|
| 443 | listvar(); |
---|
| 444 | killall("not", "int"); // kills all variables except int's (and procs) |
---|
| 445 | listvar(); |
---|
| 446 | killall(); // kills all vars except loaded procs |
---|
| 447 | listvar(); |
---|
[3d124a7] | 448 | } |
---|
| 449 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 450 | |
---|
| 451 | proc number_e (int n) |
---|
[d2b2a7] | 452 | "USAGE: number_e(n); n integer |
---|
[b42ab6] | 453 | RETURN: Euler number e=exp(1) up to n decimal digits (no rounding) |
---|
| 454 | @* - of type string if no basering of char 0 is defined |
---|
| 455 | @* - of type number if a basering of char 0 is defined |
---|
| 456 | DISPLAY: decimal format of e if printlevel > 0 (default:printlevel=0 ) |
---|
| 457 | NOTE: procedure uses algorithm of A.H.J. Sale |
---|
[3d124a7] | 458 | EXAMPLE: example number_e; shows an example |
---|
[d2b2a7] | 459 | " |
---|
[3d124a7] | 460 | { |
---|
| 461 | int i,m,s,t; |
---|
| 462 | intvec u,e; |
---|
| 463 | u[n+2]=0; e[n+1]=0; e=e+1; |
---|
| 464 | if( defined(basering) ) |
---|
| 465 | { |
---|
| 466 | if( char(basering)==0 ) { number r=2; t=1; } |
---|
| 467 | } |
---|
| 468 | string result = "2."; |
---|
| 469 | for( i=1; i<=n+1; i=i+1 ) |
---|
| 470 | { |
---|
| 471 | e = e*10; |
---|
| 472 | for( m=n+1; m>=1; m=m-1 ) |
---|
| 473 | { |
---|
| 474 | s = e[m]+u[m+1]; |
---|
[18dd47] | 475 | u[m] = s div (m+1); |
---|
[3d124a7] | 476 | e[m] = s%(m+1); |
---|
| 477 | } |
---|
| 478 | result = result+string(u[1]); |
---|
| 479 | if( t==1 ) { r = r+number(u[1])/number(10)^i; } |
---|
| 480 | } |
---|
[c860e9] | 481 | if( t==1 ) |
---|
| 482 | { dbprint(printlevel-voice+2,"// "+result[1,n+1]); |
---|
| 483 | return(r); |
---|
| 484 | } |
---|
[3d124a7] | 485 | return(result[1,n+1]); |
---|
| 486 | } |
---|
| 487 | example |
---|
| 488 | { "EXAMPLE:"; echo = 2; |
---|
[c860e9] | 489 | number_e(30);""; |
---|
[3d124a7] | 490 | ring R = 0,t,lp; |
---|
[c860e9] | 491 | number e = number_e(30); |
---|
[3d124a7] | 492 | e; |
---|
| 493 | } |
---|
| 494 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 495 | |
---|
| 496 | proc number_pi (int n) |
---|
[d2b2a7] | 497 | "USAGE: number_pi(n); n positive integer |
---|
[b42ab6] | 498 | RETURN: pi (area of unit circle) up to n decimal digits (no rounding) |
---|
| 499 | @* - of type string if no basering of char 0 is defined, |
---|
| 500 | @* - of type number, if a basering of char 0 is defined |
---|
| 501 | DISPLAY: decimal format of pi if printlevel > 0 (default:printlevel=0 ) |
---|
| 502 | NOTE: procedure uses algorithm of S. Rabinowitz |
---|
[3d124a7] | 503 | EXAMPLE: example number_pi; shows an example |
---|
[d2b2a7] | 504 | " |
---|
[3d124a7] | 505 | { |
---|
| 506 | int i,m,t,e,q,N; |
---|
| 507 | intvec r,p,B,Prelim; |
---|
| 508 | string result,prelim; |
---|
[18dd47] | 509 | N = (10*n) div 3 + 2; |
---|
[3d124a7] | 510 | p[N+1]=0; p=p+2; r=p; |
---|
| 511 | for( i=1; i<=N+1; i=i+1 ) { B[i]=2*i-1; } |
---|
| 512 | if( defined(basering) ) |
---|
| 513 | { |
---|
| 514 | if( char(basering)==0 ) { number pi; number pri; t=1; } |
---|
| 515 | } |
---|
| 516 | for( i=0; i<=n; i=i+1 ) |
---|
| 517 | { |
---|
| 518 | p = r*10; |
---|
| 519 | e = p[N+1]; |
---|
| 520 | for( m=N+1; m>=2; m=m-1 ) |
---|
| 521 | { |
---|
| 522 | r[m] = e%B[m]; |
---|
[18dd47] | 523 | q = e div B[m]; |
---|
[3d124a7] | 524 | e = q*(m-1)+p[m-1]; |
---|
| 525 | } |
---|
| 526 | r[1] = e%10; |
---|
[18dd47] | 527 | q = e div 10; |
---|
[3d124a7] | 528 | if( q!=10 and q!=9 ) |
---|
| 529 | { |
---|
| 530 | result = result+prelim; |
---|
| 531 | Prelim = q; |
---|
| 532 | prelim = string(q); |
---|
| 533 | } |
---|
| 534 | if( q==9 ) |
---|
| 535 | { |
---|
| 536 | Prelim = Prelim,9; |
---|
| 537 | prelim = prelim+"9"; |
---|
| 538 | } |
---|
| 539 | if( q==10 ) |
---|
| 540 | { |
---|
[18dd47] | 541 | Prelim = (Prelim+1)-((Prelim+1) div 10)*10; |
---|
[3d124a7] | 542 | for( m=size(Prelim); m>0; m=m-1) |
---|
| 543 | { |
---|
| 544 | prelim[m] = string(Prelim[m]); |
---|
| 545 | } |
---|
| 546 | result = result+prelim; |
---|
| 547 | if( t==1 ) { pi=pi+pri; } |
---|
| 548 | Prelim = 0; |
---|
| 549 | prelim = "0"; |
---|
| 550 | } |
---|
| 551 | if( t==1 ) { pi=pi+number(q)/number(10)^i; } |
---|
| 552 | } |
---|
| 553 | result = result,prelim[1]; |
---|
| 554 | result = "3."+result[2,n-1]; |
---|
[c860e9] | 555 | if( t==1 ) |
---|
| 556 | { dbprint(printlevel-voice+2,"// "+result); |
---|
| 557 | return(pi); |
---|
| 558 | } |
---|
[3d124a7] | 559 | return(result); |
---|
| 560 | } |
---|
| 561 | example |
---|
| 562 | { "EXAMPLE:"; echo = 2; |
---|
[c860e9] | 563 | number_pi(11);""; |
---|
| 564 | ring r = (real,10),t,dp; |
---|
| 565 | number pi = number_pi(11); pi; |
---|
[3d124a7] | 566 | } |
---|
| 567 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 568 | |
---|
| 569 | proc primes (int n, int m) |
---|
[d2b2a7] | 570 | "USAGE: primes(n,m); n,m integers |
---|
[3d124a7] | 571 | RETURN: intvec, consisting of all primes p, prime(n)<=p<=m, in increasing |
---|
[b42ab6] | 572 | order if n<=m, resp. prime(m)<=p<=n, in decreasing order if m<n. |
---|
| 573 | NOTE: prime(n); returns the biggest prime number <= min(n,32003) |
---|
| 574 | if n>=2, else 2 |
---|
[3d124a7] | 575 | EXAMPLE: example primes; shows an example |
---|
[d2b2a7] | 576 | " |
---|
[3d124a7] | 577 | { int change; |
---|
| 578 | if ( n>m ) { change=n; n=m ; m=change; change=1; } |
---|
| 579 | int q,p = prime(m),prime(n); intvec v = q; q = q-1; |
---|
| 580 | while ( q>=p ) { q = prime(q); v = q,v; q = q-1; } |
---|
| 581 | if ( change==1 ) { v = v[size(v)..1]; } |
---|
| 582 | return(v); |
---|
| 583 | } |
---|
| 584 | example |
---|
| 585 | { "EXAMPLE:"; echo = 2; |
---|
[c860e9] | 586 | primes(50,100);""; |
---|
| 587 | intvec v = primes(37,1); v; |
---|
[3d124a7] | 588 | } |
---|
| 589 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 590 | |
---|
| 591 | proc product (id, list #) |
---|
[c860e9] | 592 | "USAGE: product(id[,v]); id ideal/vector/module/matrix/intvec/intmat/list, |
---|
[b42ab6] | 593 | v intvec (default: v=1..number of entries of id) |
---|
| 594 | ASSUME: list members can be multiplied. |
---|
[65546eb] | 595 | RETURN: The product of all entries of id [with index given by v] of type |
---|
[b42ab6] | 596 | depending on the entries of id. |
---|
| 597 | NOTE: If id is not a list, id is treated as a list of polys resp. integers. |
---|
| 598 | A module m is identified with the corresponding matrix M (columns |
---|
| 599 | of M generate m). |
---|
[7708934] | 600 | @* If v is outside the range of id, we have the empty product and the |
---|
| 601 | result will be 1 (of type int). |
---|
[3d124a7] | 602 | EXAMPLE: example product; shows an example |
---|
[d2b2a7] | 603 | " |
---|
[65546eb] | 604 | { |
---|
[7708934] | 605 | //-------------------- initialization and special feature --------------------- |
---|
[c860e9] | 606 | int n,j,tt; |
---|
[65546eb] | 607 | string ty; //will become type of id |
---|
[c860e9] | 608 | list l; |
---|
[7708934] | 609 | |
---|
| 610 | // We wish to allow something like product(x(1..10)) if x(1),...,x(10) are |
---|
[65546eb] | 611 | // variables. x(1..10) is a list of polys and enters the procedure with |
---|
[7708934] | 612 | // id=x(1) and # a list with 9 polys, #[1]= x(2),...,#[9]= x(10). Hence, in |
---|
| 613 | // this case # is never empty. If an additional intvec v is given, |
---|
| 614 | // it is added to #, so we have to separate it first and make |
---|
| 615 | // the rest a list which has to be multiplied. |
---|
| 616 | |
---|
[c860e9] | 617 | int s = size(#); |
---|
| 618 | if( s!=0 ) |
---|
[65546eb] | 619 | { if ( typeof(#[s])=="intvec" or typeof(#[s])=="int") |
---|
| 620 | { |
---|
[7708934] | 621 | intvec v = #[s]; |
---|
[65546eb] | 622 | tt=1; |
---|
[7708934] | 623 | s=s-1; |
---|
[c860e9] | 624 | if ( s>0 ) { # = #[1..s]; } |
---|
| 625 | } |
---|
| 626 | } |
---|
| 627 | if ( s>0 ) |
---|
| 628 | { |
---|
[7708934] | 629 | l = list(id)+#; |
---|
| 630 | kill id; |
---|
| 631 | list id = l; //case: id = list |
---|
| 632 | ty = "list"; |
---|
| 633 | n = size(id); |
---|
[c860e9] | 634 | } |
---|
| 635 | else |
---|
[65546eb] | 636 | { |
---|
[7708934] | 637 | ty = typeof(id); |
---|
[65546eb] | 638 | if( ty == "list" ) |
---|
[7708934] | 639 | { n = size(id); } |
---|
[c860e9] | 640 | } |
---|
[7708934] | 641 | //------------------------------ reduce to 3 cases --------------------------- |
---|
[c860e9] | 642 | if( ty=="poly" or ty=="ideal" or ty=="vector" |
---|
| 643 | or ty=="module" or ty=="matrix" ) |
---|
[3d124a7] | 644 | { |
---|
| 645 | ideal i = ideal(matrix(id)); |
---|
[c860e9] | 646 | kill id; |
---|
[7708934] | 647 | ideal id = i; //case: id = ideal |
---|
| 648 | n = ncols(id); |
---|
[3d124a7] | 649 | } |
---|
[c860e9] | 650 | if( ty=="int" or ty=="intvec" or ty=="intmat" ) |
---|
[3d124a7] | 651 | { |
---|
[c860e9] | 652 | if ( ty == "int" ) { intmat S =id; } |
---|
[3d124a7] | 653 | else { intmat S = intmat(id); } |
---|
| 654 | intvec i = S[1..nrows(S),1..ncols(S)]; |
---|
[c860e9] | 655 | kill id; |
---|
[7708934] | 656 | intvec id = i; //case: id = intvec |
---|
[65546eb] | 657 | n = size(id); |
---|
[7708934] | 658 | } |
---|
| 659 | //--------------- consider intvec v and empty product ----------------------- |
---|
[65546eb] | 660 | if( tt!=0 ) |
---|
[7708934] | 661 | { |
---|
| 662 | for (j=1; j<=size(v); j++) |
---|
| 663 | { |
---|
| 664 | if ( v[j] <= 0 or v[j] > n ) //v outside range of id |
---|
[65546eb] | 665 | { |
---|
[7708934] | 666 | return(1); //empty product is 1 |
---|
[65546eb] | 667 | } |
---|
[7708934] | 668 | } |
---|
| 669 | id = id[v]; //consider part of id |
---|
| 670 | } //corresponding to v |
---|
| 671 | //--------------------- special case: one factor is zero --------------------- |
---|
| 672 | if ( typeof(id) == "ideal") |
---|
| 673 | { |
---|
| 674 | if( size(id) < ncols(id) ) |
---|
| 675 | { |
---|
| 676 | poly f; return(f); |
---|
| 677 | } |
---|
[3d124a7] | 678 | } |
---|
[7708934] | 679 | //-------------------------- finally, multiply objects ----------------------- |
---|
[65546eb] | 680 | n = size(id); |
---|
[7708934] | 681 | def f(1) = id[1]; |
---|
[c860e9] | 682 | for( j=2; j<=n; j=j+1 ) { def f(j)=f(j-1)*id[j]; } |
---|
| 683 | return(f(n)); |
---|
[3d124a7] | 684 | } |
---|
| 685 | example |
---|
| 686 | { "EXAMPLE:"; echo = 2; |
---|
| 687 | ring r= 0,(x,y,z),dp; |
---|
| 688 | ideal m = maxideal(1); |
---|
| 689 | product(m); |
---|
[c860e9] | 690 | product(m[2..3]); |
---|
[3d124a7] | 691 | matrix M[2][3] = 1,x,2,y,3,z; |
---|
| 692 | product(M); |
---|
| 693 | intvec v=2,4,6; |
---|
| 694 | product(M,v); |
---|
| 695 | intvec iv = 1,2,3,4,5,6,7,8,9; |
---|
| 696 | v=1..5,7,9; |
---|
| 697 | product(iv,v); |
---|
| 698 | intmat A[2][3] = 1,1,1,2,2,2; |
---|
| 699 | product(A,3..5); |
---|
| 700 | } |
---|
| 701 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 702 | |
---|
| 703 | proc sort (id, list #) |
---|
[a7a00b] | 704 | "USAGE: sort(id[,v,o,n]); id = ideal/module/intvec/list(of intvec's or int's) |
---|
[b42ab6] | 705 | @* sort may be called with 1, 2 or 3 arguments in the following way: |
---|
[6e52cf] | 706 | @* sort(id[,v,n]); v=intvec of positive integers, n=integer, |
---|
| 707 | @* sort(id[,o,n]); o=string (any allowed ordstr of a ring), n=integer |
---|
[b42ab6] | 708 | RETURN: a list l of two elements: |
---|
| 709 | @format |
---|
| 710 | l[1]: object of same type as input but sorted in the following way: |
---|
[3d124a7] | 711 | - if id=ideal/module: generators of id are sorted w.r.t. intvec v |
---|
| 712 | (id[v[1]] becomes 1-st, id[v[2]] 2-nd element, etc.). If no v is |
---|
| 713 | present, id is sorted w.r.t. ordering o (if o is given) or w.r.t. |
---|
| 714 | actual monomial ordering (if no o is given): |
---|
[b42ab6] | 715 | NOTE: generators with SMALLER(!) leading term come FIRST |
---|
| 716 | (e.g. sort(id); sorts backwards to actual monomial ordering) |
---|
[3d124a7] | 717 | - if id=list of intvec's or int's: consider a list element, say |
---|
| 718 | id[1]=3,2,5, as exponent vector of the monomial x^3*y^2*z^5; |
---|
| 719 | the corresponding monomials are ordered w.r.t. intvec v (s.a.). |
---|
| 720 | If no v is present, the monomials are sorted w.r.t. ordering o |
---|
| 721 | (if o is given) or w.r.t. lexicographical ordering (if no o is |
---|
| 722 | given). The corresponding ordered list of exponent vectors is |
---|
| 723 | returned. |
---|
| 724 | (e.g. sort(id); sorts lexicographically, smaller int's come first) |
---|
[a30caa3] | 725 | WARNING: Since negative exponents create the 0 polynomial in |
---|
[63be42] | 726 | Singular, id should not contain negative integers: the result |
---|
[a30caa3] | 727 | might not be as expected |
---|
[3d124a7] | 728 | - if id=intvec: id is treated as list of integers |
---|
| 729 | - if n!=0 the ordering is inverse, i.e. w.r.t. v(size(v)..1) |
---|
| 730 | default: n=0 |
---|
[b42ab6] | 731 | l[2]: intvec, describing the permutation of the input (hence l[2]=v |
---|
| 732 | if v is given (with positive integers)) |
---|
| 733 | @end format |
---|
[63be42] | 734 | NOTE: If v is given id may be any simply indexed object (e.g. any list or |
---|
| 735 | string); if v[i]<0 and i<=size(id) v[i] is set internally to i; |
---|
[f32177] | 736 | entries of v must be pairwise distinct to get a permutation id. |
---|
[3d124a7] | 737 | Zero generators of ideal/module are deleted |
---|
[d4f44f] | 738 | If 'o' is given, the input is sorted by considering leading terms |
---|
| 739 | w.r.t. the new ring ordering given by 'o' |
---|
[3d124a7] | 740 | EXAMPLE: example sort; shows an example |
---|
[d2b2a7] | 741 | " |
---|
[c860e9] | 742 | { int ii,jj,s,n = 0,0,1,0; |
---|
[3d124a7] | 743 | intvec v; |
---|
| 744 | if ( defined(basering) ) { def P = basering; } |
---|
[b5726c] | 745 | if ( size(#)==0 and (typeof(id)=="ideal" or typeof(id)=="module" |
---|
| 746 | or typeof(id)=="matrix")) |
---|
[3d124a7] | 747 | { |
---|
| 748 | id = simplify(id,2); |
---|
[558209] | 749 | for ( ii=1; ii<ncols(id); ii++ ) |
---|
[3d124a7] | 750 | { |
---|
| 751 | if ( id[ii]!=id[ii+1] ) { break;} |
---|
| 752 | } |
---|
[558209] | 753 | if ( ii != ncols(id) ) { v = sortvec(id); } |
---|
| 754 | else { v = ncols(id)..1; } |
---|
[3d124a7] | 755 | } |
---|
[b5726c] | 756 | if ( size(#)>=1 and (typeof(id)=="ideal" or typeof(id)=="module" |
---|
| 757 | or typeof(id)=="matrix") ) |
---|
[3d124a7] | 758 | { |
---|
| 759 | if ( typeof(#[1])=="string" ) |
---|
| 760 | { |
---|
[034ce1] | 761 | execute("ring r1 =("+charstr(P)+"),("+varstr(P)+"),("+#[1]+");"); |
---|
[d4f44f] | 762 | def i = imap(P,id); |
---|
[3d124a7] | 763 | v = sortvec(i); |
---|
| 764 | setring P; |
---|
| 765 | n=2; |
---|
| 766 | } |
---|
| 767 | } |
---|
| 768 | if ( typeof(id)=="intvec" or typeof(id)=="list" and n==0 ) |
---|
| 769 | { |
---|
| 770 | string o; |
---|
| 771 | if ( size(#)==0 ) { o = "lp"; n=1; } |
---|
| 772 | if ( size(#)>=1 ) |
---|
| 773 | { |
---|
| 774 | if ( typeof(#[1])=="string" ) { o = #[1]; n=1; } |
---|
| 775 | } |
---|
| 776 | } |
---|
| 777 | if ( typeof(id)=="intvec" or typeof(id)=="list" and n==1 ) |
---|
| 778 | { |
---|
| 779 | if ( typeof(id)=="list" ) |
---|
| 780 | { |
---|
| 781 | for (ii=1; ii<=size(id); ii++) |
---|
| 782 | { |
---|
| 783 | if (typeof(id[ii]) != "intvec" and typeof(id[ii]) != "int") |
---|
[bea07f] | 784 | { ERROR("// list elements must be intvec/int"); } |
---|
[3d124a7] | 785 | else |
---|
| 786 | { s=size(id[ii])*(s < size(id[ii])) + s*(s >= size(id[ii])); } |
---|
| 787 | } |
---|
| 788 | } |
---|
[034ce1] | 789 | execute("ring r=0,x(1..s),("+o+");"); |
---|
[3d124a7] | 790 | ideal i; |
---|
| 791 | poly f; |
---|
| 792 | for (ii=1; ii<=size(id); ii++) |
---|
| 793 | { |
---|
| 794 | f=1; |
---|
| 795 | for (jj=1; jj<=size(id[ii]); jj++) |
---|
| 796 | { |
---|
| 797 | f=f*x(jj)^(id[ii])[jj]; |
---|
| 798 | } |
---|
| 799 | i[ii]=f; |
---|
| 800 | } |
---|
| 801 | v = sort(i)[2]; |
---|
| 802 | } |
---|
| 803 | if ( size(#)!=0 and n==0 ) { v = #[1]; } |
---|
| 804 | if( size(#)==2 ) |
---|
| 805 | { |
---|
| 806 | if ( #[2] != 0 ) { v = v[size(v)..1]; } |
---|
| 807 | } |
---|
| 808 | s = size(v); |
---|
[63be42] | 809 | if( size(id) < s ) { s = size(id); } |
---|
[3d124a7] | 810 | def m = id; |
---|
[63be42] | 811 | if ( size(m) != 0 ) |
---|
| 812 | { |
---|
[558209] | 813 | for ( jj=1; jj<=s; jj++) |
---|
[63be42] | 814 | { |
---|
| 815 | if ( v[jj]<=0 ) { v[jj]=jj; } |
---|
| 816 | m[jj] = id[v[jj]]; |
---|
| 817 | } |
---|
| 818 | } |
---|
| 819 | if ( v == 0 ) { v = 1; } |
---|
[3d124a7] | 820 | list L=m,v; |
---|
| 821 | return(L); |
---|
| 822 | } |
---|
| 823 | example |
---|
| 824 | { "EXAMPLE:"; echo = 2; |
---|
[c860e9] | 825 | ring r0 = 0,(x,y,z,t),lp; |
---|
| 826 | ideal i = x3,z3,xyz; |
---|
[584f84d] | 827 | sort(i); //sorts using lex ordering, smaller polys come first |
---|
[65546eb] | 828 | |
---|
[c860e9] | 829 | sort(i,3..1); |
---|
[b42ab6] | 830 | |
---|
[584f84d] | 831 | sort(i,"ls")[1]; //sort w.r.t. negative lex ordering |
---|
[b42ab6] | 832 | |
---|
| 833 | intvec v =1,10..5,2..4;v; |
---|
[584f84d] | 834 | sort(v)[1]; // sort v lexicographically |
---|
[b42ab6] | 835 | |
---|
[584f84d] | 836 | sort(v,"Dp",1)[1]; // sort v w.r.t (total sum, reverse lex) |
---|
[d4f44f] | 837 | |
---|
| 838 | // Note that in general: lead(sort(M)) != sort(lead(M)), e.g: |
---|
| 839 | module M = [0, 1, 1, 0], [1, 0, 0, 1]; M; |
---|
[3f4e52] | 840 | sort(lead(M), "c, dp")[1]; |
---|
| 841 | lead(sort(M, "c, dp")[1]); |
---|
[d4f44f] | 842 | |
---|
| 843 | // In order to sort M wrt a NEW ordering by considering OLD leading |
---|
| 844 | // terms use one of the following equivalent commands: |
---|
[3f4e52] | 845 | module( M[ sort(lead(M), "c,dp")[2] ] ); |
---|
| 846 | sort( M, sort(lead(M), "c,dp")[2] )[1]; |
---|
[3d124a7] | 847 | } |
---|
| 848 | /////////////////////////////////////////////////////////////////////////////// |
---|
[15e59a] | 849 | |
---|
[84375a] | 850 | static proc lsum (int n, list l) |
---|
[15e59a] | 851 | { if (n>10) |
---|
| 852 | { return( lsum(n/2,list(l[1..(n/2)])) + lsum(n-n/2, list(l[(n/2+1)..n])) ); |
---|
| 853 | } |
---|
| 854 | else |
---|
| 855 | { def Summe=l[1]; |
---|
| 856 | for (int i=2;i<=n;i++) |
---|
| 857 | { Summe=Summe+l[i]; |
---|
| 858 | } |
---|
| 859 | return(Summe); |
---|
| 860 | } |
---|
| 861 | } |
---|
| 862 | |
---|
| 863 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 864 | |
---|
[3d124a7] | 865 | proc sum (id, list #) |
---|
[b42ab6] | 866 | "USAGE: sum(id[,v]); id ideal/vector/module/matrix/intvec/intmat/list, |
---|
| 867 | v intvec (default: v=1..number of entries of id) |
---|
| 868 | ASSUME: list members can be added. |
---|
[65546eb] | 869 | RETURN: The sum of all entries of id [with index given by v] of type |
---|
[b42ab6] | 870 | depending on the entries of id. |
---|
[7708934] | 871 | NOTE: If id is not a list, id is treated as a list of polys resp. integers. |
---|
[b42ab6] | 872 | A module m is identified with the corresponding matrix M (columns |
---|
| 873 | of M generate m). |
---|
[7708934] | 874 | @* If v is outside the range of id, we have the empty sum and the |
---|
| 875 | result will be 0 (of type int). |
---|
[3d124a7] | 876 | EXAMPLE: example sum; shows an example |
---|
[d2b2a7] | 877 | " |
---|
[3d124a7] | 878 | { |
---|
[7708934] | 879 | //-------------------- initialization and special feature --------------------- |
---|
[b42ab6] | 880 | int n,j,tt; |
---|
[7708934] | 881 | string ty; // will become type of id |
---|
[b42ab6] | 882 | list l; |
---|
[7708934] | 883 | |
---|
| 884 | // We wish to allow something like sum(x(1..10)) if x(1),...,x(10) are |
---|
[65546eb] | 885 | // variables. x(1..10) is a list of polys and enters the procedure with |
---|
[7708934] | 886 | // id=x(1) and # a list with 9 polys, #[1]= x(2),...,#[9]= x(10). Hence, in |
---|
| 887 | // this case # is never empty. If an additional intvec v is given, |
---|
| 888 | // it is added to #, so we have to separate it first and make |
---|
| 889 | // the rest a list which has to be added. |
---|
| 890 | |
---|
[b42ab6] | 891 | int s = size(#); |
---|
| 892 | if( s!=0 ) |
---|
[7708934] | 893 | { if ( typeof(#[s])=="intvec" or typeof(#[s])=="int") |
---|
[b42ab6] | 894 | { intvec v = #[s]; |
---|
[65546eb] | 895 | tt=1; |
---|
[7708934] | 896 | s=s-1; |
---|
[b42ab6] | 897 | if ( s>0 ) { # = #[1..s]; } |
---|
| 898 | } |
---|
| 899 | } |
---|
| 900 | if ( s>0 ) |
---|
| 901 | { |
---|
[7708934] | 902 | l = list(id)+#; |
---|
| 903 | kill id; |
---|
| 904 | list id = l; //case: id = list |
---|
| 905 | ty = "list"; |
---|
[b42ab6] | 906 | } |
---|
| 907 | else |
---|
[65546eb] | 908 | { |
---|
[7708934] | 909 | ty = typeof(id); |
---|
[b42ab6] | 910 | } |
---|
[7708934] | 911 | //------------------------------ reduce to 3 cases --------------------------- |
---|
[b42ab6] | 912 | if( ty=="poly" or ty=="ideal" or ty=="vector" |
---|
| 913 | or ty=="module" or ty=="matrix" ) |
---|
[7708934] | 914 | { //case: id = ideal |
---|
[3d124a7] | 915 | ideal i = ideal(matrix(id)); |
---|
[b42ab6] | 916 | kill id; |
---|
[7708934] | 917 | ideal id = simplify(i,2); //delete 0 entries |
---|
[3d124a7] | 918 | } |
---|
[b42ab6] | 919 | if( ty=="int" or ty=="intvec" or ty=="intmat" ) |
---|
[15e59a] | 920 | { //case: id = intvec |
---|
[b42ab6] | 921 | if ( ty == "int" ) { intmat S =id; } |
---|
[3d124a7] | 922 | else { intmat S = intmat(id); } |
---|
| 923 | intvec i = S[1..nrows(S),1..ncols(S)]; |
---|
[b42ab6] | 924 | kill id; |
---|
[15e59a] | 925 | intvec id = i; |
---|
[3d124a7] | 926 | } |
---|
[7708934] | 927 | //------------------- consider intvec v and empty sum ----------------------- |
---|
[65546eb] | 928 | if( tt!=0 ) |
---|
[7708934] | 929 | { |
---|
| 930 | for (j=1; j<=size(v); j++) |
---|
| 931 | { |
---|
| 932 | if ( v[j] <= 0 or v[j] > size(id) ) //v outside range of id |
---|
[65546eb] | 933 | { |
---|
[7708934] | 934 | return(0); //empty sum is 0 |
---|
[65546eb] | 935 | } |
---|
[7708934] | 936 | } |
---|
| 937 | id = id[v]; //consider part of id |
---|
| 938 | } //corresponding to v |
---|
| 939 | |
---|
| 940 | //-------------------------- finally, add objects --------------------------- |
---|
[65546eb] | 941 | n = size(id); |
---|
[15e59a] | 942 | if (n>10) |
---|
| 943 | { return( lsum(n/2,list(id[1..(n/2)])) + lsum(n-n/2, list(id[(n/2+1)..n])) ); |
---|
| 944 | } |
---|
| 945 | else |
---|
| 946 | { def Summe=id[1]; |
---|
| 947 | for (int lauf=2;lauf<=n;lauf++) |
---|
| 948 | { Summe=Summe+id[lauf]; |
---|
| 949 | } |
---|
| 950 | return(Summe); |
---|
| 951 | } |
---|
[b42ab6] | 952 | } |
---|
[3d124a7] | 953 | example |
---|
| 954 | { "EXAMPLE:"; echo = 2; |
---|
[15e59a] | 955 | ring r1 = 0,(x,y,z),dp; |
---|
[3d124a7] | 956 | vector pv = [xy,xz,yz,x2,y2,z2]; |
---|
| 957 | sum(pv); |
---|
[c860e9] | 958 | sum(pv,2..5); |
---|
| 959 | matrix M[2][3] = 1,x,2,y,3,z; |
---|
| 960 | intvec w=2,4,6; |
---|
| 961 | sum(M,w); |
---|
| 962 | intvec iv = 1,2,3,4,5,6,7,8,9; |
---|
| 963 | sum(iv,2..4); |
---|
[15e59a] | 964 | iv = intvec(1..100); |
---|
| 965 | sum(iv); |
---|
| 966 | ring r2 = 0,(x(1..10)),dp; |
---|
| 967 | sum(x(3..7),intvec(1,3,5)); |
---|
[3d124a7] | 968 | } |
---|
| 969 | /////////////////////////////////////////////////////////////////////////////// |
---|
[6f2edc] | 970 | |
---|
[15e59a] | 971 | |
---|
| 972 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 973 | |
---|
[6f2edc] | 974 | proc which (command) |
---|
[d2b2a7] | 975 | "USAGE: which(command); command = string expression |
---|
[6f2edc] | 976 | RETURN: Absolute pathname of command, if found in search path. |
---|
| 977 | Empty string, otherwise. |
---|
| 978 | NOTE: Based on the Unix command 'which'. |
---|
| 979 | EXAMPLE: example which; shows an example |
---|
[d2b2a7] | 980 | " |
---|
[6f2edc] | 981 | { |
---|
| 982 | int rs; |
---|
| 983 | int i; |
---|
[a70441f] | 984 | string fn = "which_" + string(system("pid")); |
---|
[6f2edc] | 985 | string pn; |
---|
[a70441f] | 986 | string cmd; |
---|
[82716e] | 987 | if( typeof(command) != "string") |
---|
[6f2edc] | 988 | { |
---|
[82716e] | 989 | return (pn); |
---|
[6f2edc] | 990 | } |
---|
[a70441f] | 991 | if (system("uname") != "ix86-Win") |
---|
| 992 | { |
---|
| 993 | cmd = "which "; |
---|
| 994 | } |
---|
| 995 | else |
---|
| 996 | { |
---|
| 997 | // unfortunately, it does not take -path |
---|
| 998 | cmd = "type "; |
---|
| 999 | } |
---|
| 1000 | i = system("sh", cmd + command + " > " + fn); |
---|
[6f2edc] | 1001 | pn = read(fn); |
---|
[a70441f] | 1002 | if (system("uname") != "ix86-Win") |
---|
| 1003 | { |
---|
| 1004 | // TBC: Hmm... should parse output to get rid of 'command is ' |
---|
| 1005 | pn[size(pn)] = ""; |
---|
| 1006 | i = 1; |
---|
| 1007 | while ((pn[i] != " ") and (pn[i] != "")) |
---|
| 1008 | { |
---|
| 1009 | i = i+1; |
---|
| 1010 | } |
---|
| 1011 | if (pn[i] == " ") {pn[i] = "";} |
---|
| 1012 | rs = system("sh", "ls " + pn + " > " + fn + " 2>&1 "); |
---|
| 1013 | } |
---|
| 1014 | else |
---|
[6f2edc] | 1015 | { |
---|
[a70441f] | 1016 | rs = 0; |
---|
[6f2edc] | 1017 | } |
---|
| 1018 | i = system("sh", "rm " + fn); |
---|
| 1019 | if (rs == 0) {return (pn);} |
---|
[82716e] | 1020 | else |
---|
[6f2edc] | 1021 | { |
---|
| 1022 | print (command + " not found "); |
---|
| 1023 | return (""); |
---|
| 1024 | } |
---|
| 1025 | } |
---|
| 1026 | example |
---|
| 1027 | { "EXAMPLE:"; echo = 2; |
---|
[a70441f] | 1028 | which("sh"); |
---|
[6f2edc] | 1029 | } |
---|
| 1030 | /////////////////////////////////////////////////////////////////////////////// |
---|
[ebbe4a] | 1031 | |
---|
| 1032 | proc watchdog(int i, string cmd) |
---|
[a7a00b] | 1033 | "USAGE: watchdog(i,cmd); i integer, cmd string |
---|
[b42ab6] | 1034 | RETURN: Result of cmd, if the result can be computed in i seconds. |
---|
| 1035 | Otherwise the computation is interrupted after i seconds, |
---|
| 1036 | the string "Killed" is returned and the global variable |
---|
| 1037 | 'watchdog_interrupt' is defined. |
---|
[65546eb] | 1038 | NOTE: * the MP package must be enabled |
---|
| 1039 | * the current basering should not be watchdog_rneu, since |
---|
[b42ab6] | 1040 | watchdog_rneu will be killed |
---|
[ebbe4a] | 1041 | * if there are variable names of the structure x(i) all |
---|
| 1042 | polynomials have to be put into eval(...) in order to be |
---|
| 1043 | interpreted correctly |
---|
[a6606e6] | 1044 | * a second Singular process is started by this procedure |
---|
[ebbe4a] | 1045 | EXAMPLE: example watchdog; shows an example |
---|
| 1046 | " |
---|
| 1047 | { |
---|
| 1048 | string rname=nameof(basering); |
---|
[17ee4f] | 1049 | def rsave=basering; |
---|
[ebbe4a] | 1050 | if (defined(watchdog_rneu)) |
---|
| 1051 | { |
---|
| 1052 | kill watchdog_rneu; |
---|
| 1053 | } |
---|
| 1054 | // If we do not have MP-links, watchdog cannot be used |
---|
| 1055 | if (system("with","MP")) |
---|
| 1056 | { |
---|
| 1057 | if ( i > 0 ) |
---|
| 1058 | { |
---|
| 1059 | int j=10; |
---|
| 1060 | int k=999999; |
---|
[65546eb] | 1061 | // fork, get the pid of the child and send it the command |
---|
[ebbe4a] | 1062 | link l_fork="MPtcp:fork"; |
---|
| 1063 | open(l_fork); |
---|
| 1064 | write(l_fork,quote(system("pid"))); |
---|
| 1065 | int pid=read(l_fork); |
---|
| 1066 | execute("write(l_fork,quote(" + cmd + "));"); |
---|
| 1067 | |
---|
| 1068 | |
---|
| 1069 | // sleep in small, but growing intervals for appr. 1 second |
---|
| 1070 | while(j < k) |
---|
| 1071 | { |
---|
| 1072 | if (status(l_fork, "read", "ready", j)) {break;} |
---|
| 1073 | j = j + j; |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | // sleep in intervals of one second |
---|
| 1077 | j = 1; |
---|
| 1078 | if (!status(l_fork,"read","ready")) |
---|
| 1079 | { |
---|
| 1080 | while (j < i) |
---|
| 1081 | { |
---|
| 1082 | if (status(l_fork, "read", "ready", k)) {break;} |
---|
| 1083 | j = j + 1; |
---|
| 1084 | } |
---|
| 1085 | } |
---|
| 1086 | // check, whether we have a result, and return it |
---|
| 1087 | if (status(l_fork, "read", "ready")) |
---|
| 1088 | { |
---|
| 1089 | def result = read(l_fork); |
---|
| 1090 | if (nameof(basering)!=rname) |
---|
| 1091 | { |
---|
| 1092 | def watchdog_rneu=basering; |
---|
[17ee4f] | 1093 | setring rsave; |
---|
[7f3ad4] | 1094 | if (!defined(result)) |
---|
| 1095 | { |
---|
| 1096 | def result=fetch(watchdog_rneu,result); |
---|
| 1097 | } |
---|
[ebbe4a] | 1098 | } |
---|
| 1099 | if(defined(watchdog_interrupt)) |
---|
| 1100 | { |
---|
[3b77465] | 1101 | kill watchdog_interrupt; |
---|
[ebbe4a] | 1102 | } |
---|
| 1103 | close(l_fork); |
---|
| 1104 | } |
---|
| 1105 | else |
---|
| 1106 | { |
---|
| 1107 | string result="Killed"; |
---|
| 1108 | if(!defined(watchdog_interrupt)) |
---|
| 1109 | { |
---|
| 1110 | int watchdog_interrupt=1; |
---|
| 1111 | export watchdog_interrupt; |
---|
| 1112 | } |
---|
| 1113 | close(l_fork); |
---|
| 1114 | j = system("sh","kill " + string(pid)); |
---|
| 1115 | } |
---|
| 1116 | return(result); |
---|
| 1117 | } |
---|
| 1118 | else |
---|
| 1119 | { |
---|
| 1120 | ERROR("First argument of watchdog has to be a positive integer."); |
---|
| 1121 | } |
---|
[50cbdc] | 1122 | } |
---|
| 1123 | else |
---|
| 1124 | { |
---|
[ebbe4a] | 1125 | ERROR("MP-support is not enabled in this version of Singular."); |
---|
[65546eb] | 1126 | } |
---|
[ebbe4a] | 1127 | } |
---|
| 1128 | example |
---|
| 1129 | { "EXAMPLE:"; echo=2; |
---|
| 1130 | ring r=0,(x,y,z),dp; |
---|
| 1131 | poly f=x^30+y^30; |
---|
| 1132 | watchdog(1,"factorize(eval("+string(f)+"))"); |
---|
| 1133 | watchdog(100,"factorize(eval("+string(f)+"))"); |
---|
| 1134 | } |
---|
| 1135 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 1136 | |
---|
| 1137 | proc deleteSublist(intvec v,list l) |
---|
[803c5a1] | 1138 | "USAGE: deleteSublist(v,l); intvec v; list l |
---|
[ebbe4a] | 1139 | where the entries of the integer vector v correspond to the |
---|
| 1140 | positions of the elements to be deleted |
---|
| 1141 | RETURN: list without the deleted elements |
---|
| 1142 | EXAMPLE: example deleteSublist; shows an example" |
---|
| 1143 | { |
---|
| 1144 | list k; |
---|
| 1145 | int i,j,skip; |
---|
| 1146 | j=1; |
---|
| 1147 | skip=0; |
---|
| 1148 | intvec vs=sort(v)[1]; |
---|
| 1149 | for ( i=1 ; i <=size(vs) ; i++) |
---|
| 1150 | { |
---|
| 1151 | while ((j+skip) < vs[i]) |
---|
| 1152 | { |
---|
| 1153 | k[j] = l[j+skip]; |
---|
| 1154 | j++; |
---|
| 1155 | } |
---|
| 1156 | skip++; |
---|
| 1157 | } |
---|
| 1158 | if(vs[size(vs)]<size(l)) |
---|
| 1159 | { |
---|
| 1160 | k=k+list(l[(vs[size(vs)]+1)..size(l)]); |
---|
| 1161 | } |
---|
| 1162 | return(k); |
---|
| 1163 | } |
---|
| 1164 | example |
---|
| 1165 | { "EXAMPLE:"; echo=2; |
---|
| 1166 | list l=1,2,3,4,5; |
---|
| 1167 | intvec v=1,3,4; |
---|
| 1168 | l=deleteSublist(v,l); |
---|
| 1169 | l; |
---|
| 1170 | } |
---|
[8b87364] | 1171 | |
---|
| 1172 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 1173 | proc primecoeffs(J, list #) |
---|
[a7a00b] | 1174 | "USAGE: primecoeffs(J[,p]); J any type which can be converted to a matrix |
---|
[8b87364] | 1175 | e.g. ideal, matrix, vector, module, int, intvec |
---|
[a7a00b] | 1176 | p = integer |
---|
[c94e60f] | 1177 | COMPUTE: primefactors <= p of coeffs of J (default p = 32003) |
---|
[a7a00b] | 1178 | RETURN: a list, say l, of two intvectors:@* |
---|
| 1179 | l[1] : the different primefactors of all coefficients of J@* |
---|
[8b87364] | 1180 | l[2] : the different remaining factors |
---|
| 1181 | EXAMPLE: example primecoeffs; shows an example |
---|
| 1182 | " |
---|
| 1183 | { |
---|
| 1184 | int q,ii,n,mark;; |
---|
[298d0a] | 1185 | if (size(#) == 0) |
---|
[8b87364] | 1186 | { |
---|
[298d0a] | 1187 | q=32003; |
---|
[8b87364] | 1188 | } |
---|
[298d0a] | 1189 | else |
---|
[8b87364] | 1190 | { |
---|
| 1191 | if( typeof(#[1]) != "int") |
---|
| 1192 | { |
---|
| 1193 | ERROR("2nd parameter must be of type int"+newline); |
---|
| 1194 | } |
---|
| 1195 | q=#[1]; |
---|
[be8dbb] | 1196 | if (q > 32003) { q = 32003; } |
---|
[8b87364] | 1197 | } |
---|
| 1198 | |
---|
| 1199 | if (defined(basering) == 0) |
---|
| 1200 | { |
---|
| 1201 | mark=1; |
---|
| 1202 | ring r = 0,x,dp; |
---|
| 1203 | } |
---|
| 1204 | def I = ideal(matrix(J)); |
---|
| 1205 | poly p = product(maxideal(1)); |
---|
[298d0a] | 1206 | matrix Coef=coef(I[1],p); |
---|
[8b87364] | 1207 | ideal id, jd, rest; |
---|
| 1208 | intvec v,re; |
---|
| 1209 | list result,l; |
---|
| 1210 | for(ii=2; ii<=ncols(I); ii++) |
---|
| 1211 | { |
---|
| 1212 | Coef=concat(Coef,coef(I[ii],p)); |
---|
| 1213 | } |
---|
| 1214 | id = Coef[2,1..ncols(Coef)]; |
---|
| 1215 | id = simplify(id,6); |
---|
[298d0a] | 1216 | for (ii=1; ii<=size(id); ii++) |
---|
| 1217 | { |
---|
| 1218 | l = primefactors(number(id[ii]),q); |
---|
[c94e60f] | 1219 | list jdl=l[2]; |
---|
| 1220 | jd = jd,jdl[1..size(jdl)]; |
---|
| 1221 | kill jdl; |
---|
| 1222 | rest=rest, l[1]; |
---|
[298d0a] | 1223 | } |
---|
[8b87364] | 1224 | jd = simplify(jd,6); |
---|
[298d0a] | 1225 | for (ii=1; ii<=size(jd); ii++) |
---|
| 1226 | { |
---|
[8b87364] | 1227 | v[ii]=int(jd[ii]); |
---|
| 1228 | } |
---|
| 1229 | v = sort(v)[1]; |
---|
| 1230 | rest = simplify(rest,6); |
---|
| 1231 | id = sort(id)[1]; |
---|
| 1232 | if (mark) |
---|
| 1233 | { |
---|
| 1234 | for (ii=1; ii<=size(rest); ii++) |
---|
| 1235 | { |
---|
| 1236 | re[ii] = int(rest[ii]); |
---|
| 1237 | } |
---|
| 1238 | result = v,re; |
---|
| 1239 | } |
---|
| 1240 | else |
---|
| 1241 | { |
---|
[298d0a] | 1242 | result = v,rest; |
---|
[8b87364] | 1243 | } |
---|
| 1244 | return(result); |
---|
| 1245 | } |
---|
| 1246 | example |
---|
| 1247 | { "EXAMPLE:"; echo = 2; |
---|
| 1248 | primecoeffs(intvec(7*8*121,7*8));""; |
---|
| 1249 | ring r = 0,(b,c,t),dp; |
---|
| 1250 | ideal I = -13b6c3t+4b5c4t,-10b4c2t-5b4ct2; |
---|
| 1251 | primecoeffs(I); |
---|
[298d0a] | 1252 | } |
---|
[8b87364] | 1253 | /////////////////////////////////////////////////////////////////////////////// |
---|
[90d772] | 1254 | proc timeFactorize(poly i,list #) |
---|
[a7a00b] | 1255 | "USAGE: timeFactorize(p,d); poly p , integer d |
---|
[3c4dcc] | 1256 | RETURN: factorize(p) if the factorization finished after d-1 |
---|
[90d772] | 1257 | seconds otherwhise f is considered to be irreducible |
---|
| 1258 | EXAMPLE: example timeFactorize; shows an example |
---|
| 1259 | " |
---|
| 1260 | { |
---|
| 1261 | def P=basering; |
---|
| 1262 | if (size(#) > 0) |
---|
| 1263 | { |
---|
| 1264 | if (system("with", "MP")) |
---|
| 1265 | { |
---|
| 1266 | if ((typeof(#[1]) == "int")&&(#[1])) |
---|
| 1267 | { |
---|
| 1268 | int wait = #[1]; |
---|
| 1269 | int j = 10; |
---|
| 1270 | |
---|
| 1271 | string bs = nameof(basering); |
---|
| 1272 | link l_fork = "MPtcp:fork"; |
---|
| 1273 | open(l_fork); |
---|
| 1274 | write(l_fork, quote(system("pid"))); |
---|
| 1275 | int pid = read(l_fork); |
---|
| 1276 | write(l_fork, quote(timeFactorize(eval(i)))); |
---|
| 1277 | |
---|
| 1278 | // sleep in small intervalls for appr. one second |
---|
| 1279 | if (wait > 0) |
---|
| 1280 | { |
---|
| 1281 | while(j < 1000000) |
---|
| 1282 | { |
---|
| 1283 | if (status(l_fork, "read", "ready", j)) {break;} |
---|
| 1284 | j = j + j; |
---|
| 1285 | } |
---|
| 1286 | } |
---|
| 1287 | |
---|
| 1288 | // sleep in intervalls of one second from now on |
---|
| 1289 | j = 1; |
---|
| 1290 | while (j < wait) |
---|
| 1291 | { |
---|
| 1292 | if (status(l_fork, "read", "ready", 1000000)) {break;} |
---|
| 1293 | j = j + 1; |
---|
| 1294 | } |
---|
| 1295 | |
---|
| 1296 | if (status(l_fork, "read", "ready")) |
---|
| 1297 | { |
---|
| 1298 | def result = read(l_fork); |
---|
| 1299 | if (bs != nameof(basering)) |
---|
| 1300 | { |
---|
| 1301 | def PP = basering; |
---|
| 1302 | setring P; |
---|
| 1303 | def result = imap(PP, result); |
---|
| 1304 | kill PP; |
---|
| 1305 | } |
---|
[3b77465] | 1306 | kill l_fork; |
---|
[90d772] | 1307 | } |
---|
| 1308 | else |
---|
| 1309 | { |
---|
| 1310 | list result; |
---|
| 1311 | intvec v=1,1; |
---|
| 1312 | result[1]=list(1,i); |
---|
| 1313 | result[2]=v; |
---|
| 1314 | j = system("sh", "kill " + string(pid)); |
---|
| 1315 | } |
---|
| 1316 | return (result); |
---|
| 1317 | } |
---|
| 1318 | } |
---|
| 1319 | } |
---|
| 1320 | return(factorH(i)); |
---|
| 1321 | } |
---|
| 1322 | example |
---|
| 1323 | { "EXAMPLE:"; echo = 2; |
---|
| 1324 | ring r=0,(x,y),dp; |
---|
| 1325 | poly p=((x2+y3)^2+xy6)*((x3+y2)^2+x10y); |
---|
| 1326 | p=p^2; |
---|
| 1327 | //timeFactorize(p,2); |
---|
| 1328 | //timeFactorize(p,20); |
---|
| 1329 | } |
---|
| 1330 | |
---|
| 1331 | proc timeStd(ideal i,list #) |
---|
| 1332 | "USAGE: timeStd(i,d), i ideal, d integer |
---|
| 1333 | RETURN: std(i) if the standard basis computation finished after |
---|
| 1334 | d-1 seconds and i otherwhise |
---|
| 1335 | EXAMPLE: example timeStd; shows an example |
---|
| 1336 | " |
---|
| 1337 | { |
---|
| 1338 | def P=basering; |
---|
| 1339 | if (size(#) > 0) |
---|
| 1340 | { |
---|
| 1341 | if (system("with", "MP")) |
---|
| 1342 | { |
---|
| 1343 | if ((typeof(#[1]) == "int")&&(#[1])) |
---|
| 1344 | { |
---|
| 1345 | int wait = #[1]; |
---|
| 1346 | int j = 10; |
---|
| 1347 | |
---|
| 1348 | string bs = nameof(basering); |
---|
| 1349 | link l_fork = "MPtcp:fork"; |
---|
| 1350 | open(l_fork); |
---|
| 1351 | write(l_fork, quote(system("pid"))); |
---|
| 1352 | int pid = read(l_fork); |
---|
| 1353 | write(l_fork, quote(timeStd(eval(i)))); |
---|
| 1354 | |
---|
| 1355 | // sleep in small intervalls for appr. one second |
---|
| 1356 | if (wait > 0) |
---|
| 1357 | { |
---|
| 1358 | while(j < 1000000) |
---|
| 1359 | { |
---|
| 1360 | if (status(l_fork, "read", "ready", j)) {break;} |
---|
| 1361 | j = j + j; |
---|
| 1362 | } |
---|
| 1363 | } |
---|
| 1364 | j = 1; |
---|
| 1365 | while (j < wait) |
---|
| 1366 | { |
---|
| 1367 | if (status(l_fork, "read", "ready", 1000000)) {break;} |
---|
| 1368 | j = j + 1; |
---|
| 1369 | } |
---|
| 1370 | if (status(l_fork, "read", "ready")) |
---|
| 1371 | { |
---|
| 1372 | def result = read(l_fork); |
---|
| 1373 | if (bs != nameof(basering)) |
---|
| 1374 | { |
---|
| 1375 | def PP = basering; |
---|
| 1376 | setring P; |
---|
| 1377 | def result = imap(PP, result); |
---|
| 1378 | kill PP; |
---|
| 1379 | } |
---|
[3b77465] | 1380 | kill l_fork; |
---|
[90d772] | 1381 | } |
---|
| 1382 | else |
---|
| 1383 | { |
---|
| 1384 | ideal result=i; |
---|
| 1385 | j = system("sh", "kill " + string(pid)); |
---|
| 1386 | } |
---|
| 1387 | return (result); |
---|
| 1388 | } |
---|
| 1389 | } |
---|
| 1390 | } |
---|
| 1391 | return(std(i)); |
---|
| 1392 | } |
---|
| 1393 | example |
---|
| 1394 | { "EXAMPLE:"; echo = 2; |
---|
| 1395 | ring r=32003,(a,b,c,d,e),dp; |
---|
| 1396 | int n=6; |
---|
| 1397 | ideal i= |
---|
| 1398 | a^n-b^n, |
---|
| 1399 | b^n-c^n, |
---|
| 1400 | c^n-d^n, |
---|
| 1401 | d^n-e^n, |
---|
| 1402 | a^(n-1)*b+b^(n-1)*c+c^(n-1)*d+d^(n-1)*e+e^(n-1)*a; |
---|
| 1403 | timeStd(i,2); |
---|
| 1404 | timeStd(i,20); |
---|
| 1405 | } |
---|
| 1406 | |
---|
| 1407 | proc factorH(poly p) |
---|
| 1408 | "USAGE: factorH(p) p poly |
---|
| 1409 | RETURN: factorize(p) |
---|
[a7a00b] | 1410 | NOTE: changes variables to make the last variable the principal |
---|
[90d772] | 1411 | one in the multivariate factorization and factorizes then |
---|
| 1412 | the polynomial |
---|
| 1413 | EXAMPLE: example factorH; shows an example |
---|
| 1414 | " |
---|
| 1415 | { |
---|
| 1416 | def R=basering; |
---|
| 1417 | int i,j; |
---|
| 1418 | int n=1; |
---|
| 1419 | int d=nrows(coeffs(p,var(1))); |
---|
| 1420 | for(i=1;i<=nvars(R);i++) |
---|
| 1421 | { |
---|
| 1422 | j=nrows(coeffs(p,var(i))); |
---|
| 1423 | if(d>j) |
---|
| 1424 | { |
---|
| 1425 | n=i; |
---|
| 1426 | d=j; |
---|
| 1427 | } |
---|
| 1428 | } |
---|
| 1429 | ideal ma=maxideal(1); //die letzte Variable ist die Hauptvariable |
---|
| 1430 | ma[nvars(R)]=var(n); |
---|
| 1431 | ma[n]=var(nvars(R)); |
---|
| 1432 | map phi=R,ma; |
---|
| 1433 | list fac=factorize(phi(p)); |
---|
| 1434 | list re=phi(fac); |
---|
| 1435 | return(re); |
---|
| 1436 | } |
---|
| 1437 | example |
---|
| 1438 | { "EXAMPLE:"; echo = 2; |
---|
| 1439 | system("random",992851144); |
---|
| 1440 | ring r=32003,(x,y,z,w,t),lp; |
---|
| 1441 | poly p=y2w9+yz7t-yz5w4-z2w4t4-w8t3; |
---|
| 1442 | factorize(p); //fast |
---|
| 1443 | system("random",992851262); |
---|
| 1444 | //factorize(p); //slow |
---|
| 1445 | system("random",992851262); |
---|
| 1446 | factorH(p); |
---|
| 1447 | } |
---|