Changeset 194409 in git
 Timestamp:
 Apr 22, 2013, 2:19:46 PM (10 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'ad2543eab51733612ba7d118afc77edca719600e')
 Children:
 6fcd65b41235516be599e23554d96064636cb46c
 Parents:
 809d634e3370e14c61f7b1ee234231400c570c0f
 gitauthor:
 Martin Lee <martinlee84@web.de>20130422 14:19:46+02:00
 gitcommitter:
 Martin Lee <martinlee84@web.de>20130502 11:42:40+02:00
 File:

 1 edited
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Singular/LIB/absfact.lib
r809d63 r194409 26 26 PROCEDURES: 27 27 absFactorize(); absolute factorization of poly 28 absBiFactorize(); absolute factorization of bivariate poly 28 29 "; 29 30 … … 609 610 } 610 611 612 //////////////////////////////////////////////////////////////////////////////// 611 613 proc absBiFactorize(poly p, list #) 614 "USAGE: absBiFactorize(p [,s]); p poly, s string 615 ASSUME: coefficient field is the field of rational numbers or a 616 transcendental extension thereof 617 RETURN: ring @code{R} which is obtained from the current basering 618 by adding a new parameter (if a string @code{s} is given as a 619 second input, the new parameter gets this string as name). The ring 620 @code{R} comes with a list @code{absolute_factors} with the 621 following entries: 622 @format 623 absolute_factors[1]: ideal (the absolute factors) 624 absolute_factors[2]: intvec (the multiplicities) 625 absolute_factors[3]: ideal (the minimal polynomials) 626 absolute_factors[4]: int (total number of nontriv. absolute factors) 627 @end format 628 The entry @code{absolute_factors[1][1]} is a constant, the 629 entry @code{absolute_factors[3][1]} is the parameter added to the 630 current ring.@* 631 Each of the remaining entries @code{absolute_factors[1][j]} stands for 632 a class of conjugated absolute factors. The corresponding entry 633 @code{absolute_factors[3][j]} is the minimal polynomial of the 634 field extension over which the factor is minimally defined (its degree 635 is the number of conjugates in the class). If the entry 636 @code{absolute_factors[3][j]} coincides with @code{absolute_factors[3][1]}, 637 no field extension was necessary for the @code{j}th (class of) 638 absolute factor(s). 639 NOTE: The input polynomial p is assumed to be bivariate or to contain one para 640 meter and one variable. All factors are presented denominator and 641 contentfree. The constant factor (first entry) is chosen such that the 642 product of all (!) the (denominator and contentfree) absolute factors 643 of @code{p} equals @code{p / absolute_factors[1][1]}. 644 SEE ALSO: factorize, absPrimdecGTZ, absFactorize 645 EXAMPLE: example absBiFactorize; shows an example 646 " 612 647 { 613 648 int dblevel = printlevel  voice + 2; … … 726 761 } 727 762 728 MPo;729 763 list tmpf=absBiFact (p); 730 764 … … 784 818 785 819 dbprint( printlevelvoice+3," 786 // 'abs Factorize' created a ring, in which a list absolute_factors (the820 // 'absBiFactorize' created a ring, in which a list absolute_factors (the 787 821 // absolute factors) is stored. 788 822 // To access the list of absolute factors, type (if the name S was assigned … … 790 824 setring(S); absolute_factors; "); 791 825 return(MPo); 826 } 827 example 828 { 829 "EXAMPLE:"; echo = 2; 830 ring R = (0), (x,y), lp; 831 poly p = (7*x^2 + 2*x*y^2 + 6*x + y^4 + 14*y^2 + 47)*(5x2+y2)^3*(xy)^4; 832 def S = absBiFactorize(p) ; 833 setring(S); 834 absolute_factors; 792 835 } 793 836
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