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dimensionIP -- compute the dimension of a monomial ideal using integer programming

Synopsis

Description

This function calls codimensionIP and then returns $n$-codimensionIP($I$), where $n$ is the number of variables in the polynomial ring where $I$ is defined. The integer programming input and output files created will therefore be named "codim.zpl", "codim.errors", etc. as with codimensionIP.

i1 : R = QQ[x,y,z,w,v];
 
i2 : I = monomialIdeal(x*y*w, x*z*v, y*x, y*z*v);

o2 : MonomialIdeal of R
 
i3 : dimensionIP(I)
Codim files saved in directory: /tmp/M2-9918-0/0

o3 = 3

The location of input/output files for SCIP solving is printed to the screen by default. To change this, see ScipPrintLevel.

i4 : ScipPrintLevel = 0;
 
i5 : J = monomialIdeal(x*y^3*z^7, y^4*w*v, z^2*v^8, x*w^3*v^3, y^10, z^10)

                     10     3 7   10   4        3 3   2 8
o5 = monomialIdeal (y  , x*y z , z  , y w*v, x*w v , z v )

o5 : MonomialIdeal of R
 
i6 : dimensionIP(J)

o6 = 2

The dimension of a monomial ideal is equal to the dimension of its radical. Therefore, when looking at the IP formulation written to the temporary file "codim.zpl", you will see that exponents are ignored.

See also

Ways to use dimensionIP :

For the programmer

The object dimensionIP is a method function.