RegularChains[ChainTools]
NumberOfSolutions
number of solutions of a regular chain
Calling Sequence
Parameters
Description
Examples
NumberOfSolutions(rc, R)
rc
-
regular chain of R
R
polynomial ring
The command NumberOfSolutions(rc, R) returns the number of complex solutions of rc.
If rc has a positive dimension, then infinity is returned.
If rc has dimension zero, the number of roots is returned.
This command is part of the RegularChains[ChainTools] package, so it can be used in the form NumberOfSolutions(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][NumberOfSolutions](..).
withRegularChains:
withChainTools:
R≔PolynomialRingx,a,b,c
R≔polynomial_ring
sys≔ax2+bx+c
dec≔Triangularizesys,R,output=lazard
dec≔regular_chain,regular_chain
mapEquations,dec,R
ax2+bx+c,bx+c,a
mapDimension,dec,R
1,0
mapNumberOfSolutions,dec,R
∞,1
See Also
Dimension
Equations
PolynomialRing
RegularChains
SeparateSolutions
Triangularize
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