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D.15.30.14 invertLeftFraction
Procedure from library olga.lib (see olga_lib).
- Usage:
- invertLeftFraction(frac, locType, locData), vector frac, int locType,
list/vector/intvec locData
- Purpose:
- invert a fraction in the specified localization
- Assume:
- frac is invertible in the loc. specified by locType and locData
- Return:
- vector
- Note:
- - returns the multiplicative inverse of frac in the localization
specified by locType and locData,
- throws error if frac is not invertible (NOTE: this does NOT mean
that the fraction is not invertible, it just means it could not be
determined by the method listed above).
Example:
| | LIB "olga.lib";
ring R = 0,(x,y,Dx,Dy),dp;
def S = Weyl();
setring S; S;
==> // coefficients: QQ
==> // number of vars : 4
==> // block 1 : ordering dp
==> // : names x y Dx Dy
==> // block 2 : ordering C
==> // noncommutative relations:
==> // Dxx=x*Dx+1
==> // Dyy=y*Dy+1
poly g1 = x+3;
poly g2 = x*y;
list L = g1,g2;
vector frac = [g1*g2, 17, 0, 0];
print(invertLeftFraction(frac, 0, L));
==> [17,x^2*y+3*x*y]
ideal p = x-1, y;
frac = [g1, x, 0, 0];
print(invertLeftFraction(frac, 1, p));
==> [x,x+3]
intvec rat = 1,2;
frac = [g1*g2, y, 0, 0];
print(invertLeftFraction(frac, 2, rat));
==> [y,x^2*y+3*x*y]
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