# poly(String) -- make a polynomial using classic Macaulay syntax

## Synopsis

• Function: poly
• Usage:
poly s
• Inputs:
• s,
• Outputs:
• , created from s using classic Macaulay syntax, as described in Classic

## Description

 i1 : R = ZZ/32003[a..d,x_1..x_4,y_(1,1)..y_(2,2)]; i2 : poly "a2b-3ab-1" 2 o2 = a b - 3a*b - 1 o2 : R i3 : poly "a2y[1,1]3-3ab-1" 2 3 o3 = a y - 3a*b - 1 1,1 o3 : R i4 : poly "(a+b)(a+2c)" 2 o4 = a + a*b + 2a*c + 2b*c o4 : R i5 : poly "(a+b+c)3-1" 3 2 2 3 2 2 2 2 3 o5 = a + 3a b + 3a*b + b + 3a c + 6a*b*c + 3b c + 3a*c + 3b*c + c - 1 o5 : R i6 : poly "3/4a2b-3ab-1" 2 o6 = - 8000a b - 3a*b - 1 o6 : R i7 : poly "a5+5a4b+10a3b2+10a2b3+5ab4+b5-10a4c-40a3bc-60a2b2c-40ab3c-10b4c" 5 4 3 2 2 3 4 5 4 3 2 2 o7 = a + 5a b + 10a b + 10a b + 5a*b + b - 10a c - 40a b*c - 60a b c - ------------------------------------------------------------------------ 3 4 40a*b c - 10b c o7 : R i8 : poly "(a+(c+y[1,1])2)2-1" 4 3 2 2 3 4 2 2 o8 = c + 4c y + 6c y + 4c*y + y + 2a*c + 4a*c*y + 2a*y + 1,1 1,1 1,1 1,1 1,1 1,1 ------------------------------------------------------------------------ 2 a - 1 o8 : R

## Ways to use this method:

• poly(String) -- make a polynomial using classic Macaulay syntax