Changeset c335c5 in git
- Timestamp:
- Apr 6, 2009, 3:21:58 PM (14 years ago)
- Branches:
- (u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
- Children:
- c1f6a9ca685ae005c4cbd13e1df1355305542a7c
- Parents:
- 08e081516771eec845058a046616a8c0d7e8325b
- File:
-
- 1 edited
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Singular/LIB/zeroset.lib
r08e081 rc335c5 1 1 // Last change 12.02.2001 (Eric Westenberger) 2 2 /////////////////////////////////////////////////////////////////////////////// 3 version="$Id: zeroset.lib,v 1. 19 2009-04-06 09:17:01 seelischExp $";3 version="$Id: zeroset.lib,v 1.20 2009-04-06 13:21:58 Singular Exp $"; 4 4 category="Symbolic-numerical solving"; 5 5 info=" … … 18 18 of Singular for univariate factorization of polynomials over simple algebraic 19 19 extensions in characteristic 0. 20 20 21 21 NOTE: 22 22 Subprocedures with postfix 'Main' require that the ring contains a variable … … 25 25 26 26 PROCEDURES: 27 quotient(f, g) quotient q of f w.r.t. g (in f = q*g + remainder)27 Quotient(f, g) quotient q of f w.r.t. g (in f = q*g + remainder) 28 28 remainder(f,g) remainder of the division of f by g 29 29 roots(f) computes all roots of f in an extension field of Q … … 470 470 /////////////////////////////////////////////////////////////////////////////// 471 471 472 proc quotient(poly f, poly g)473 "USAGE: quotient(f, g); where f,g are polynomials;472 proc Quotient(poly f, poly g) 473 "USAGE: Quotient(f, g); where f,g are polynomials; 474 474 PURPOSE: compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < deg(g) 475 475 RETURN: list of polynomials … … 480 480 ASSUME: basering = Q[x] or Q(a)[x] 481 481 NOTE: outdated, use div/mod instead 482 EXAMPLE: example quotient; shows an example482 EXAMPLE: example Quotient; shows an example 483 483 " 484 484 { … … 502 502 poly f = x4 - 2; 503 503 poly g = x - a; 504 list qr = quotient(f, g);504 list qr = Quotient(f, g); 505 505 qr; 506 506 qr[1]*g + qr[2] - f; … … 518 518 this represents the ring Q(a)[x] together with its minimal polynomial. 519 519 NOTE: outdated, use div/mod instead 520 EXAMPLE: example quotient; shows an example521 520 " 522 521 {
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