reduced vector has fewer entries than original vector (is this correct?)

[Johannes Rauh (jrauh@…]

In the following example, reduction of a vector with 18 entries yields a vector with 15 entries. Are the "missing" 3 entries zero? But then, why are not all zero-entries omitted.

SINGULAR /

A Computer Algebra System for Polynomial Computations / version 3-1-0

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by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Mar 2009

FB Mathematik der Universitaet, D-67653 Kaiserslautern \

. ring R = 0,(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11),(c,dp);

. poly P0 = x0 + x4 + x6 + x8;

poly P1 = - x0 + x1 - x4 + x5 - x8 + x9; poly P2 = - x1 - x5 - x9; poly P3 = - x0 + x2 - x6 + x7 - x8 + x10; poly P4 = x0 - x1 - x2 + x3 + x8 - x9 - x10 + x11; poly P5 = x1 - x3 + x9 - x11; poly P6 = - x2 - x7 - x10; poly P7 = x2 - x3 + x10 - x11; poly P8 = x3 + x11; poly P9 = - x4 - x6 - x8; poly P10 = x4 - x5 + x8 - x9; poly P11 = x5 + x9; poly P12 = x6 - x7 + x8 - x10; poly P13 = - x8 + x9 + x10 - x11; poly P14 = - x9 + x11; poly P15 = x7 + x10; poly P16 = - x10 + x11; poly P17 = - x11;

. ideal J = x11,x10,x9-1,x8-2,x7,x6+3,x5+4,x4+2,x3,x2,x1,x0;

. vector P = [P0, P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P 15, P16, P17];

printf ("%s", reduce (P, std(J)));

[-3,-3,3,1,1,1,0,0,0,3,3,-3,-1,-1,-1]

[seelisch]

answered by Oleksandr and Anne