Changeset 69ac6d in git for Tst/Short/alexpoly.tst


Ignore:
Timestamp:
Mar 14, 2003, 3:15:08 PM (21 years ago)
Author:
Thomas Markwig <keilen@…>
Branches:
(u'spielwiese', '2a584933abf2a2d3082034c7586d38bb6de1a30a')
Children:
bec956d6a49dd1f0d9ed365803f93d650975500f
Parents:
8ee1228e66840c68cbe2297c95e628539f0cb729
Message:
Neue Fassung.


git-svn-id: file:///usr/local/Singular/svn/trunk@6612 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Tst/Short/alexpoly.tst

    r8ee122 r69ac6d  
    44tst_init();
    55LIB "alexpoly.lib";
    6 // ------------ test of resolutiongraph: -------------------
    76ring r=0,(x,y),ds;
    8 poly f1=x2-y2;
    9 poly f2=x2+y+y2;
    10 poly f3=(x2+y3)*(x2+y3+xy2);
    11 resolutiongraph(f1);
    12 resolutiongraph(f2);
    13 resolutiongraph(f3);
    14 resolutiongraph(2x2+3xy+4xy3-x2y);
    15 resolutiongraph(x3-y5);
     7//////////////////////////////////////////////////////////////////////////
     8//  Defining examples.
     9//////////////////////////////////////////////////////////////////////////
     10//  Examples of polynomials
     11/////////////////////////////////////////////////////////////////////////
     12list f;
     13f[1] =x2-y2;
     14f[2] =x2+y+y2;
     15f[3] =(x2+y3)*(x2+y3+xy2);
     16f[4] =-x27-x25-15x24y-30x23y2+5x20y3-135x19y4+3x18y5-10x15y6-90x14y7+10x10y9-3x9y10-5x5y12+y15;
     17f[5] =x5-y11;
     18f[6] =xy8+y8+x4y6+4x3y6+2x5y5+6x6y4+4x8y3+x10y2+4x9y2+2x11y+x12;
     19f[7] =(x6-y4);
     20f[8] =(((y-x2+x3)*(y-x2-x3)));
     21f[9] =((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5));
     22f[10]=((y2-x3)*(y2-x3-x4));
     23f[11]=((y2-x3-x4)*(y2+x3+x4));
     24f[12]=(((x2-y)^2+x5)*((2x2-y)^2+x5));
     25f[13]=((x2-y4)*(x+y4));
     26f[14]=-x9+x8-6x7y+3x6y2-2x4y3-3x3y4+y6;
     27f[15]=-x21+x20-8x18y-4x15y2-8x13y3+6x10y4-4x5y6+y8;
     28f[16]=-x19+x18-12x17y-6x15y2-40x14y3+15x12y4-12x11y5-20x9y6+15x6y8-6x3y10+y12;
     29f[17]=x22-x21-14x20y+7x18y2-70x17y3-21x15y4-42x14y5+35x12y6-2x11y7-35x9y8+21x6y10-7x3y12+y14;
     30f[18]=-x17-2x16-x15-20x13y2+5x12y2-10x10y4-10x9y4+10x6y6-5x3y8+y10;
     31f[19]=(f[16]*f[17]*f[18]);
     32f[20]=((x2-y3)*(x3-y5)*(x5-y7)*(x7-y11)*(x11-y13));
     33f[21]=((x3+3x2y-xy4+y10)*(x3-x2y+y8));
     34f[22]=-x11+x10-4x8y-2x5y2+y4;
     35f[23]=x7-y8;
     36f[24]=x15-y16;
     37f[25]=f[1]*f[2];
     38f[26]=f[2]*f[3];
     39f[27]=f[4]*f[5];
     40f[28]=f[1]*f[2]*f[3]*f[4]*f[5];
     41f[29]=f[14]*f[15];
     42f[30]=f[6]*f[7];
     43f[31]=f[6]*f[8]*f[12];
     44f[32]=2x2+3xy+4xy3-x2y;
     45f[33]=(x-y)*(x-2y)*(x-3y)*(x-4y);
     46f[34]=(x-y)*(x-2y)*(x-3y)*(x-4y)*(x-5y);
     47f[35]=(x7-y3)*(y4-2x3y2-4x5y+x6-x7)*(x2-y11);
     48f[36]=-x23-2x22-x21-42x19y2+7x18y2-70x16y4-21x15y4-14x13y6+35x12y6-35x9y8+21x6y10-7x3y12+y14;
     49f[37]=-x29-x28+7x24y-21x20y2+35x16y3-35x12y4+21x8y5-7x4y6+y7;
     50
    1651poly p_1 = y2+x3;
    1752poly p_2 = p_1^2 + x5y;
    … …  
    1954poly p_4 = p_3^2 + x^20 *p_2;
    2055poly p_5 = p_4^2 + x^40 *p_3;
    21 resolutiongraph(p_1*p_2*p_3);
    22 resolutiongraph(p_5*p_3);
    23 resolutiongraph((x7-y3)*(y4-2x3y2-4x5y+x6-x7)*(x2-y11));
    24 poly heme=xy8+y8+x4y6+4x3y6+2x5y5+6x6y4+4x8y3+x10y2+4x9y2+2x11y+x12;
    25 list hne=develop(heme);
     56
     57f[38]=p_1;
     58f[39]=p_2;
     59f[40]=p_3;
     60f[41]=p_4;
     61f[42]=p_5;
     62f[43]=p_1*p_2*p_3;
     63f[44]=p_3*p_5;
     64
     65f[45]=(-x7+x6-4x5y-2x3y2+y4)*(-x21+x20-12x19y-30x17y2-4x15y3+3x14y4-48x12y5+6x10y6-3x7y8-4x5y9+y12);
     66f[46]=f[16]*f[17]*f[18]*f[22]*f[23]*f[24];
     67f[47]=(x5-y7)*(x10-y17);
     68f[48]=(x5-y7)*(x13-y23);
     69
     70list f_irr=x-y,x+y,y-x2+x3,y2-x3-x4,(x2-y)^2+x5,(2x2-y)^2+x5,x-y2,x+y2,x+y4,x3-y5,x5-y7,x7-y11,x11-y13,f[2],f[4],f[5],f[6],f[14],f[15],f[16],f[17],f[18],f[22],f[23],f[24],f[36],f[37],f[38],f[39],f[40],f[41],f[42],(-x7+x6-4x5y-2x3y2+y4),(-x21+x20-12x19y-30x17y2-4x15y3+3x14y4-48x12y5+6x10y6-3x7y8-4x5y9+y12);
     71
     72///////////////////////////////////////////////////////////////////////////////////////////
     73// Defining the invariants of the above examples.
     74///////////////////////////////////////////////////////////////////////////////////////////
     75list FF;
     76//Polynomial: f[1]=x2-y2
     77FF[1]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(1),intvec(1)));
     78//Polynomial: f[2]=y+x2+y2
     79FF[2]=list(intmat(intvec(0),1,1),list(intvec(1)));
     80//Polynomial: f[3]=x4+x3y2+2x2y3+xy5+y6
     81FF[3]=list(intmat(intvec(0,4,4,0),2,2),list(intvec(2,3),intvec(2,3)));
     82//Polynomial: f[4]=y15-5x5y12+10x10y9-3x9y10-10x15y6-90x14y7+5x20y3-135x19y4+3x18y5-x25-15x24y-30x23y2-x27
     83FF[4]=list(intmat(intvec(0),1,1),list(intvec(15,25,27)));
     84//Polynomial: f[5]=x5-y11
     85FF[5]=list(intmat(intvec(0),1,1),list(intvec(5,11)));
     86//Polynomial: f[6]=y8+4x3y6+xy8+6x6y4+2x5y5+x4y6+4x9y2+4x8y3+x12+2x11y+x10y2
     87FF[6]=list(intmat(intvec(0),1,1),list(intvec(8,12,14,15)));
     88//Polynomial: f[7]=-y4+x6
     89FF[7]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(2,3),intvec(2,3)));
     90//Polynomial: f[8]=y2-2x2y+x4-x6
     91FF[8]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(1),intvec(1)));
     92//Polynomial: f[9]=4x2y8-5xy9+y10-12x5y6+6x4y7+13x8y4-2x7y5-6x11y2+x14
     93FF[9]=list(intmat(intvec(0,1,1,1,1,0,1,1,1,1,0,3,1,1,3,0),4,4),list(intvec(1),intvec(1),intvec(4,6,7),intvec(4,6,7)));
     94//Polynomial: f[10]=y4-2x3y2+x6-x4y2+x7
     95FF[10]=list(intmat(intvec(0,5,5,0),2,2),list(intvec(2,3),intvec(2,3)));
     96//Polynomial: f[11]=y4-x6-2x7-x8
     97FF[11]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(2,3),intvec(2,3)));
     98//Polynomial: f[12]=y4-6x2y3+13x4y2-12x6y+2x5y2+4x8-6x7y+5x9+x10
     99FF[12]=list(intmat(intvec(0,2,2,0),2,2),list(intvec(2,5),intvec(2,5)));
     100//Polynomial: f[13]=x3-xy4+x2y4-y8
     101FF[13]=list(intmat(intvec(0,2,2,2,0,2,2,2,0),3,3),list(intvec(1),intvec(1),intvec(1)));
     102//Polynomial: f[14]=y6-2x4y3-3x3y4+x8-6x7y+3x6y2-x9
     103FF[14]=list(intmat(intvec(0),1,1),list(intvec(6,8,9)));
     104//Polynomial: f[15]=y8-4x5y6+6x10y4-8x13y3-4x15y2-8x18y+x20-x21
     105FF[15]=list(intmat(intvec(0),1,1),list(intvec(8,20,21)));
     106//Polynomial: f[16]=y12-6x3y10+15x6y8-20x9y6+15x12y4-12x11y5-6x15y2-40x14y3+x18-12x17y-x19
     107FF[16]=list(intmat(intvec(0),1,1),list(intvec(12,18,19)));
     108//Polynomial: f[17]=y14-7x3y12+21x6y10-35x9y8+35x12y6-2x11y7-21x15y4-42x14y5+7x18y2-70x17y3-x21-14x20y+x22
     109FF[17]=list(intmat(intvec(0),1,1),list(intvec(14,21,22)));
     110//Polynomial: f[18]=y10-5x3y8+10x6y6-10x9y4+5x12y2-10x10y4-x15-20x13y2-2x16-x17
     111FF[18]=list(intmat(intvec(0),1,1),list(intvec(10,15,17)));
     112//Polynomial: f[19]
     113FF[19]=list(intmat(intvec(0,9,6,9,0,6,6,6,0),3,3),list(intvec(14,21,22),intvec(12,18,19),intvec(10,15,17)));
     114//Polynomial: f[20]
     115FF[20]=list(intmat(intvec(0,4,3,3,3,4,0,3,3,3,3,3,0,3,3,3,3,3,0,4,3,3,3,4,0),5,5),list(intvec(11,13),intvec(5,7),intvec(2,3),intvec(7,11),intvec(3,5)));
     116//Polynomial: f[21]=x6+2x5y-3x4y2-x4y4+x3y5+x3y8+3x2y9+x3y10-x2y11-xy12+y18
     117FF[21]=list(intmat(intvec(0,1,1,1,1,1,0,1,1,1,1,1,0,3,3,1,1,3,0,4,1,1,3,4,0),5,5),list(intvec(1),intvec(1),intvec(1),intvec(2,7),intvec(1)));
     118//Polynomial: f[22]=y4-2x5y2-4x8y+x10-x11
     119FF[22]=list(intmat(intvec(0),1,1),list(intvec(4,10,11)));
     120//Polynomial: f[23]=x7-y8
     121FF[23]=list(intmat(intvec(0),1,1),list(intvec(7,8)));
     122//Polynomial: f[24]=x15-y16
     123FF[24]=list(intmat(intvec(0),1,1),list(intvec(15,16)));
     124//Polynomial: f[25]=x2y-y3+x4-y4
     125FF[25]=list(intmat(intvec(0,1,1,1,0,1,1,1,0),3,3),list(intvec(1),intvec(1),intvec(1)));
     126//Polynomial: f[26]=x4y+x6+x4y2+x3y3+2x2y4+x5y2+2x4y3+x3y4+2x2y5+xy6+y7+x3y5+x2y6+xy7+y8
     127FF[26]=list(intmat(intvec(0,1,1,1,0,4,1,4,0),3,3),list(intvec(1),intvec(2,3),intvec(2,3)));
     128//Polynomial: f[27]
     129FF[27]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(15,25,27),intvec(5,11)));
     130//Polynomial: f[28]
     131FF[28]=list(intmat(intvec(0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,2,1,1,1,1,1,2,0,1,1,1,1,1,1,1,0,4,2,1,1,1,1,4,0,2,1,1,1,1,2,2,0),7,7),list(intvec(1),intvec(1),intvec(15,25,27),intvec(1),intvec(2,3),intvec(2,3),intvec(5,11)));
     132//Polynomial: f[29]
     133FF[29]=list(intmat(intvec(0,2,2,0),2,2),list(intvec(6,8,9),intvec(8,20,21)));
     134//Polynomial: f[30]=-y12-4x3y10-xy12-5x6y8-2x5y9-x4y10-4x8y7+x7y8+5x12y4+4x15y2+4x14y3+x18+2x17y+x16y2
     135FF[30]=list(intmat(intvec(0,3,3,3,0,4,3,4,0),3,3),list(intvec(2,3),intvec(2,3),intvec(8,12,14,15)));
     136//Polynomial: f[31]
     137FF[31]=list(intmat(intvec(0,2,2,2,2,2,0,2,2,2,2,2,0,3,3,2,2,3,0,3,2,2,3,3,0),5,5),list(intvec(8,12,14,15),intvec(2,5),intvec(2,5),intvec(1),intvec(1)));
     138//Polynomial: f[32]=2x2+3xy-x2y+4xy3
     139FF[32]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(1),intvec(1)));
     140//Polynomial: f[33]=x4-10x3y+35x2y2-50xy3+24y4
     141FF[33]=list(intmat(intvec(0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0),4,4),list(intvec(1),intvec(1),intvec(1),intvec(1)));
     142//Polynomial: f[34]=x5-15x4y+85x3y2-225x2y3+274xy4-120y5
     143FF[34]=list(intmat(intvec(0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0),5,5),list(intvec(1),intvec(1),intvec(1),intvec(1),intvec(1)));
     144//Polynomial: f[35]
     145FF[35]=list(intmat(intvec(0,2,1,2,0,1,1,1,0),3,3),list(intvec(4,6,7),intvec(3,7),intvec(2,11)));
     146//Polynomial: f[36]=y14-7x3y12+21x6y10-35x9y8+35x12y6-21x15y4-14x13y6+7x18y2-70x16y4-x21-42x19y2-2x22-x23
     147FF[36]=list(intmat(intvec(0),1,1),list(intvec(14,21,23)));
     148//Polynomial: f[37]=y7-7x4y6+21x8y5-35x12y4+35x16y3-21x20y2+7x24y-x28-x29
     149FF[37]=list(intmat(intvec(0),1,1),list(intvec(7,29)));
     150//Polynomial: f[38]=y2+x3
     151FF[38]=list(intmat(intvec(0),1,1),list(intvec(2,3)));
     152//Polynomial: f[39]=y4+2x3y2+x6+x5y
     153FF[39]=list(intmat(intvec(0),1,1),list(intvec(4,6,7)));
     154//Polynomial: f[40]=y8+4x3y6+6x6y4+2x5y5+4x9y2+4x8y3+x12+2x11y+2x10y2+x13
     155FF[40]=list(intmat(intvec(0),1,1),list(intvec(8,12,14,15)));
     156//Polynomial: f[41]
     157FF[41]=list(intmat(intvec(0),1,1),list(intvec(16,24,28,30,31)));
     158//Polynomial: f[42]
     159FF[42]=list(intmat(intvec(0),1,1),list(intvec(32,48,56,60,62,63)));
     160//Polynomial: f[43]
     161FF[43]=list(intmat(intvec(0,4,4,4,0,6,4,6,0),3,3),list(intvec(2,3),intvec(8,12,14,15),intvec(4,6,7)));
     162//Polynomial: f[44]
     163FF[44]=list(intmat(intvec(0,8,8,0),2,2),list(intvec(32,48,56,60,62,63),intvec(8,12,14,15)));
     164//Polynomial: f[45]
     165FF[45]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(4,6,7),intvec(12,20,21)));
     166//Polynomial: f[46]
     167FF[46]=list(intmat(intvec(0,1,1,2,2,2,1,0,8,1,1,1,1,8,0,1,1,1,2,1,1,0,9,6,2,1,1,9,0,6,2,1,1,6,6,0),6,6),list(intvec(4,10,11),intvec(7,8),intvec(15,16),intvec(12,18,19),intvec(14,21,22),intvec(10,15,17)));
     168//Polynomial: f[47]=(x5-y7)(x10-y17)
     169FF[47]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(5,7),intvec(10,17)));
     170//Polynomial: f[48]=(x5-y7)(x13-y23)
     171FF[48]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(5,7),intvec(13,23)));
     172
     173
     174//////////////////////////////////////////////////////////////////////////////////////
     175/// Examples, created from f_irr
     176//////////////////////////////////////////////////////////////////////////////////////
     177// Consider the product of all the polynomials in f_irr.
     178// Polynomial: (x-y) (x+y) (y-x2+x3) (y2-x3-x4) (y2-2x2y+x4+x5) (y2-4x2y+4x4+x5) (x-y2) (x+y2) (x+y4) (x3-y5) (x5-y7) (x7-y11) (x11-y13) (y+x2+y2) (y15-5x5y12+10x10y9-3x9y10-10x15y6-90x14y7+5x20y3-135x19y4+3x18y5-x25-15x24y-30x23y2-x27) (x5-y11) (y8+4x3y6+xy8+6x6y4+2x5y5+x4y6+4x9y2+4x8y3+x12+2x11y+x10y2) (y6-2x4y3-3x3y4+x8-6x7y+3x6y2-x9) (y8-4x5y6+6x10y4-8x13y3-4x15y2-8x18y+x20-x21) (y12-6x3y10+15x6y8-20x9y6+15x12y4-12x11y5-6x15y2-40x14y3+x18-12x17y-x19) (y14-7x3y12+21x6y10-35x9y8+35x12y6-2x11y7-21x15y4-42x14y5+7x18y2-70x17y3-x21-14x20y+x22) (y10-5x3y8+10x6y6-10x9y4+5x12y2-10x10y4-x15-20x13y2-2x16-x17) (y4-2x5y2-4x8y+x10-x11) (x7-y8) (x15-y16) (y14-7x3y12+21x6y10-35x9y8+35x12y6-21x15y4-14x13y6+7x18y2-70x16y4-x21-42x19y2-2x22-x23) (y7-7x4y6+21x8y5-35x12y4+35x16y3-21x20y2+7x24y-x28-x29) (y2+x3) (y4+2x3y2+x6+x5y) (y8+4x3y6+6x6y4+2x5y5+4x9y2+4x8y3+x12+2x11y+2x10y2+x13) (y16+8x3y14+28x6y12+4x5y13+56x9y10+24x8y11+70x12y8+60x11y9+8x10y10+56x15y6+80x14y7+34x13y8+28x18y4+60x17y5+56x16y6+8x15y7+8x21y2+24x20y3+44x19y4+20x18y5+x24+4x23y+16x22y2+16x21y3+5x20y4+2x25+4x24y+6x23y2+2x26+x25y) (y32+16x3y30+120x6y28+8x5y29+560x9y26+112x8y27+1820x12y24+728x11y25+32x10y26+4368x15y22+2912x14y23+388x13y24+8008x18y20+8008x17y21+2160x16y22+80x15y23+11440x21y18+16016x20y19+7304x19y20+824x18y21+12870x24y16+24024x23y17+16720x22y18+3840x21y19+138x20y20+11440x27y14+27456x26y15+27324x25y16+10680x24y17+1180x23y18+8008x30y12+24024x29y13+32736x28y14+19680x27y15+4480x26y16+170x25y17+4368x33y10+16016x32y11+29040x31y12+25200x30y13+9920x29y14+1168x28y15+1820x36y8+8008x35y9+19008x34y10+22848x33y11+14140x32y12+3472x31y13+152x30y14+560x39y6+2912x38y7+9020x37y8+14640x36y9+13496x35y10+5824x34y11+804x33y12+120x42y4+728x41y5+2992x40y6+6480x39y7+8680x38y8+6020x37y9+1776x36y10+96x35y11+16x45y2+112x44y3+648x43y4+1880x42y5+3680x41y6+3920x40y7+2112x39y8+364x38y9+x48+8x47y+80x46y2+320x45y3+970x44y4+1568x43y5+1448x42y6+544x41y7+42x40y8+4x49+24x48y+140x47y2+352x46y3+564x45y4+400x44y5+104x43y6+8x50+34x49y+112x48y2+144x47y3+94x46y4+12x45y5+8x51+20x50y+36x49y2+16x48y3+5x52+6x51y+3x50y2+x53) (y4-2x3y2+x6-4x5y-x7) (y12-4x5y9-3x7y8+6x10y6-48x12y5-4x15y3+3x14y4-30x17y2+x20-12x19y-x21)
     179FF[49]=list(intmat(intvec(0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,3,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,0,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,4,4,4,2,1,1,4,2,3,3,3,3,3,4,3,1,1,3,2,0,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,2,2,0,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,0,2,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,0,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,0,2,2,2,2,1,1,3,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,0,3,4,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,0,3,4,1,1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,3,0,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,3,0,1,1,2,1,1,1,1,1,1,1,7,7,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,0,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,3,2,2,1,1,1,1,1,1,1,2,0,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,7,1,1,1,1,1,1,2,2,3,2,2,2,2,1,1,0,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,0,3,2,3,3,3,2,1,1,3,2,4,6,7,7,7,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,3,0,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,0,2,2,2,6,1,1,2,3,2,2,2,2,2,2,2,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,0,9,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,9,0,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,6,6,0,2,1,1,6,2,3,3,3,3,3,5,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,6,2,2,2,0,1,1,2,3,2,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,0,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,8,0,1,1,1,1,1,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,7,7,6,2,1,1,0,2,3,3,3,3,3,5,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,3,2,2,2,3,1,1,2,0,2,2,2,2,2,2,2,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,4,3,2,3,3,3,2,1,1,3,2,0,4,4,4,4,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,6,3,2,3,3,3,2,1,1,3,2,4,0,6,6,6,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,0,8,8,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,0,10,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,10,0,3,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,5,5,5,2,1,1,5,2,3,3,3,3,3,0,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,7,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,0 ),34,34),list(intvec(1),intvec(1),intvec(1),intvec(2,3),intvec(2,5),intvec(2,5),intvec(1),intvec(1),intvec(1),intvec(3,5),intvec(5,7),intvec(7,11),intvec(11,13),intvec(1),intvec(15,25,27),intvec(5,11),intvec(8,12,14,15),intvec(6,8,9),intvec(8,20,21),intvec(12,18,19),intvec(14,21,22),intvec(10,15,17),intvec(4,10,11),intvec(7,8),intvec(15,16),intvec(14,21,23),intvec(7,29),intvec(2,3),intvec(4,6,7),intvec(8,12,14,15),intvec(16,24,28,30,31),intvec(32,48,56,60,62,63),intvec(4,6,7),intvec(12,20,21)));
     180
     181/////////////////////////////////////////////////////////////////////////////////////
     182/// Examples of characteristic exponents
     183/////////////////////////////////////////////////////////////////////////////////////
     184list vv;
     185vv[1]=intvec(18,27,75,125);
     186vv[2]=intvec(27,36,60,100);
     187vv[3]=intvec(2,3);
     188vv[4]=intvec(3,7);
     189vv[5]=intvec(4,6,7);
     190vv[6]=intvec(5,8);
     191vv[7]=intvec(6,15,19);
     192vv[8]=intvec(7,16);
     193vv[9]=intvec(8,12,30,34);
     194vv[10]=intvec(9,21,23);
     195vv[11]=intvec(10,35,41);
     196vv[12]=intvec(30,115,1001);
     197vv[13]=intvec(100,150,375,420,672);
     198vv[14]]=intvec(8,20,30,31);
     199
     200/////////////////////////////////////////////////////////////////////////////////////
     201/// Examples of multiplicity sequences
     202/////////////////////////////////////////////////////////////////////////////////////
     203list w;
     204w[1]=intvec(2,1,1);
     205w[2]=intvec(3,3,1,1,1);
     206w[3]=intvec(4,2,2,1,1);
     207w[4]=intvec(5,3,2,1,1);
     208w[5]=intvec(6,6,3,3,3,1,1,1);
     209w[6]=intvec(7,7,2,2,2,1,1);
     210w[7]=intvec(8,4,4,4,4,4,4,2,2,2,2);
     211w[8]=intvec(9,9,3,3,3,2,1,1);
     212w[9]=intvec(10,10,10,5,5,5,1,1,1,1,1);
     213w[10]=intvec(30,30,30,25,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1);
     214w[11]=intvec(100,50,50,50,50,50,50,25,25,25,20,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,2,2,1,1);
     215w[12]=intvec(8,8,4,4,4,4,2,2,1,1);
     216w[13]=intvec(18,9,9,9,9,9,9,9,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1);
     217w[14]=intvec(27,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1);
     218w[15]=intvec(36,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1);
     219w[16]=intvec(21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1);
     220
     221// ------------ test of resolutiongraph: -------------------
     222resolutiongraph(f[1]);
     223resolutiongraph(f[2]);
     224resolutiongraph(FF[3]);
     225resolutiongraph(FF[32]);
     226resolutiongraph(FF[33]);
     227resolutiongraph(FF[43]);
     228resolutiongraph(FF[44]);
     229resolutiongraph(FF[35]);
     230list hne=develop(f[6]);
    26231resolutiongraph(hne);
    27 resolutiongraph(-x23-2x22-x21-42x19y2+7x18y2-70x16y4-21x15y4-14x13y6+35x12y6-35x9y8+21x6y10-7x3y12+y14);
    28 resolutiongraph(-x29-x28+7x24y-21x20y2+35x16y3-35x12y4+21x8y5-7x4y6+y7);
     232resolutiongraph(f[36]);
     233resolutiongraph(FF[37]);
    29234intvec v=6,9,16;
    30235resolutiongraph(v);
    … …  
    41246resolutiongraph(list(M2,list(u1,u2,u3)));
    42247// ------------ test of totalmultiplicities: -------------------
    43 totalmultiplicities(x6-y4);
    44 totalmultiplicities(hnexpansion((y-x2+x3)*(y-x2-x3)));
    45 totalmultiplicities((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5));
    46 totalmultiplicities((y2-x3)*(y2-x3-x4));
    47 totalmultiplicities((y2-x3-x4)*(y2+x3+x4));
    48 totalmultiplicities(((x2-y)^2+x5)*((2x2-y)^2+x5));
    49 totalmultiplicities((x2-y4)*(x+y4));
    50 poly g1=-x9+x8-6x7y+3x6y2-2x4y3-3x3y4+y6;
    51 poly g2=-x21+x20-8x18y-4x15y2-8x13y3+6x10y4-4x5y6+y8;
    52 totalmultiplicities(g1*g2);
    53 poly k1=-x19+x18-12x17y-6x15y2-40x14y3+15x12y4-12x11y5-20x9y6+15x6y8-6x3y10+y12;
    54 poly k2=x22-x21-14x20y+7x18y2-70x17y3-21x15y4-42x14y5+35x12y6-2x11y7
    55 -35x9y8+21x6y10-7x3y12+y14;
    56 poly k3=-x17-2x16-x15-20x13y2+5x12y2-10x10y4-10x9y4+10x6y6-5x3y8+y10;
    57 totalmultiplicities(k1*k2*k3);
    58 totalmultiplicities((x2-y3)*(x3-y5)*(x5-y7)*(x7-y11)*(x11-y13));
    59 totalmultiplicities((x3+3x2y-xy4+y10)*(x3-x2y+y8));
     248totalmultiplicities(f[7]);
     249totalmultiplicities(hnexpansion(f[8]));
     250totalmultiplicities(f[9]);
     251totalmultiplicities(FF[10]);
     252totalmultiplicities(FF[11]);
     253totalmultiplicities(FF[12]);
     254totalmultiplicities(FF[13]);
     255totalmultiplicities(f[14]*f[15]);
     256totalmultiplicities(f[16]*f[17]*f[18]);
     257totalmultiplicities(FF[20]);
     258totalmultiplicities(FF[21]);
    60259intmat m1[2][2]=0,10,10,0;
    61260intvec v3=9,10;
    … …  
    69268totalmultiplicities(list(M2,list(z1,z2,z3)));
    70269// ------------ test of alexanderpolynomial: -------------------
    71 poly h1=-x11+x10-4x8y-2x5y2+y4;
    72 poly h2=x7-y8;
    73 poly h3=x15-y16;
    74 list ALEX=alexanderpolynomial(h1*h2);
     270list ALEX=alexanderpolynomial(f[22]*f[23]);
    75271def ALEXring=ALEX[1];
    76272setring ALEXring;
    … …  
    81277setring r;
    82278kill ALEXring;
    83 ALEX=alexanderpolynomial(h1*h2*h3);
     279ALEX=alexanderpolynomial(f[22]*f[23]*f[24]);
    84280def ALEXring=ALEX[1];
    85281setring ALEXring;
    … …  
    100296setring r;
    101297kill ALEXring;
    102 poly ff1=-x27-x25-15x24y-30x23y2+5x20y3-135x19y4+3x18y5-10x15y6-90x14y7
    103 +10x10y9-3x9y10-5x5y12+y15;
    104 poly ff2=x5-y11;
    105 ALEX=alexanderpolynomial(hnexpansion(ff1*ff2));
     298ALEX=alexanderpolynomial(hnexpansion(f[4]*f[5]));
    106299def ALEXring=ALEX[1];
    107300setring ALEXring;
    … …  
    112305setring r;
    113306kill ALEXring;
     307// ------------ test of semigroup:  ------------------
     308semigroup(intvec(18,27,75,125));
     309semigroup(f[24]);
     310for (int i=1;i<=48;i++)
     311{
     312  semigroup(FF[i]);
     313}
    114314// ------------ test of charexp2multseq:  ------------------
    115 intvec vv=8,20,30,31;
    116 charexp2multseq(vv);
    117 intvec vv1=18,27,75,125;
    118 charexp2multseq(vv1);
    119 intvec vv2=27,36,60,100;
    120 charexp2multseq(vv2);
    121 intvec vv3=2,3;
    122 charexp2multseq(vv3);
    123 intvec vv4=3,7;
    124 charexp2multseq(vv4);
    125 intvec vv5=4,6,7;
    126 charexp2multseq(vv5);
    127 intvec vv6=5,8;
    128 charexp2multseq(vv6);
    129 intvec vv7=6,15,19;;
    130 charexp2multseq(vv7);
    131 intvec vv8=7,16;
    132 charexp2multseq(vv8);
    133 intvec vv9=8,12,30,34;
    134 charexp2multseq(vv9);
    135 intvec vv10=9,21,23;
    136 charexp2multseq(vv10);
    137 intvec vv11=10,35,41;;
    138 charexp2multseq(vv11);
    139 intvec vv12=30,115,1001;
    140 charexp2multseq(vv12);
    141 intvec vv13=100,150,375,420,672;
    142 charexp2multseq(vv13);
     315for (i=1;i<=14;i++)
     316{
     317  charexp2multseq(vv[i]);
     318}
     319// ------------ test of charexp2generators: ------------------------
     320for (i=1;i<=14;i++)
     321{
     322  charexp2generators(vv[i]);
     323}
     324// ------------ test of charexp2inter: ------------------------
     325charexp2inter(intmat(intvec(0,1,1,0),2,2),list(vv[3],vv[4]));
     326charexp2inter(intmat(intvec(0,4,4,0),2,2),list(vv[2],vv[4]));
     327charexp2inter(intmat(intvec(0,1,3,1,0,2,3,2,0),2,2),list(vv[13],vv[4],vv[9]));
     328// ------------ test of charexp2conductor: ------------------------
     329for (i=1;i<=14;i++)
     330{
     331  charexp2conductor(vv[i]);
     332}
    143333// ------------ test of multseq2charexp: ------------------------
    144 intvec w1=2,1,1;
    145 intvec w2=3,3,1,1,1;
    146 intvec w3=4,2,2,1,1;
    147 intvec w4=5,3,2,1,1 ;
    148 intvec w5=6,6,3,3,3,1,1,1 ;
    149 intvec w6=7,7,2,2,2,1,1;
    150 intvec w7=8,4,4,4,4,4,4,2,2,2,2 ;
    151 intvec w8=9,9,3,3,3,2,1,1 ;
    152 intvec w9=10,10,10,5,5,5,1,1,1,1,1 ;
    153 intvec w10=30,30,30,25,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1;
    154 intvec w11=100,50,50,50,50,50,50,25,25,25,20,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,2,2,1,1 ;
    155 intvec w12=8,8,4,4,4,4,2,2,1,1;
    156 intvec w13=18,9,9,9,9,9,9,9,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1;
    157 intvec w14=27,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1;
    158 intvec w15=36,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
    159 intvec w16=21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1;
    160 list L3=w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16;
    161 for (int i=1;i<=16;i++)
    162 {
    163   multseq2charexp(L3[i]);
     334for (i=1;i<=16;i++)
     335{
     336  multseq2charexp(w[i]);
    164337}
    165338// ------------ test of charexp2poly: -------------------
    … …  
    182355  tau_es(hnexpansion(y*(x^2-y^i)));
    183356}
    184 tau_es((x-y)*(x-2y)*(x-3y)*(x-4y));
    185 tau_es((x-y)*(x-2y)*(x-3y)*(x-4y)*(x-5y));
     357tau_es(FF[33]));
     358tau_es(FF[34]);
     359for (i=1;i<=size(FF);i++)
     360{
     361  tau_es(FF[i]);
     362}
    186363tau_es(a1);
    187364tau_es(L2);
    188365// --------------- additions: -----------------------------
     366example resolutiongraph;
    189367example totalmultiplicities;
    190368example alexanderpolynomial;
     369example semigroup;
    191370example charexp2multseq;
    192371example multseq2charexp;
     372example charexp2generators;
     373example charexp2inter;
     374example charexp2conductor;
    193375example charexp2poly;
    194376example tau_es;
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