# normaliz(List) -- calls Normaliz with several input matrices

## Synopsis

• Function: normaliz
• Usage:
normaliz L
• Inputs:
• a list, a list of pairs (mat,nmzType)
• Optional inputs:
• allComputations => ..., default value false
• grading => ..., default value {}
• Outputs:
• an instance of the type RationalCone, generators of the integral closure and optional output from Normaliz

## Description

This function applies Normaliz to all mat each in the type set by the second parameter nmzType. The function returns an object of type RationalCone defined by the file with suffix gen , if computed, and possibly some additional information.It is possibly to give several matrices of the same type. All matrices of one type are then appended to one matrix by Normaliz.

By default, the cone returned contains only the content of the output file .gen, under the key "gen", i.e. the generators that have been computed, line by line and the content of the output file .inv, under the key "inv".

 i1 : hy=matrix {{-1,0,-1,0,3,0,0,0,0},{-1,0,1,0,1,0,0,0,0},{1,0,1,0,-1,0,0,0,0},{1,0,-1,0,1,0,0,0,0}}; 4 9 o1 : Matrix ZZ <--- ZZ i2 : eq=matrix {{1,1,1,-1,-1,-1,0,0,0},{1,1,1,0,0,0,-1,-1,-1},{0,1,1,-1,0, 0,-1,0,0},{1,0,1,0,-1,0,0,-1,0},{1,1,0,0,0,-1,0,0,-1},{0,1,1,0,-1,0,0,0,-1},{1,1,0,0,-1,0,-1,0,0}}; 7 9 o2 : Matrix ZZ <--- ZZ i3 : cg=matrix {{1,0,0,0,0,0,0,0,0,2},{0,0,1,0,0,0,0,0,0,2},{0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,1,2}}; 4 10 o3 : Matrix ZZ <--- ZZ i4 : rc=normaliz({(hy,"inequalities"),(eq,"equations"),(cg,"congruences")}); i5 : rc#"gen" o5 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 2 2 2 2 2 2 2 2 | | 2 3 4 5 3 1 2 3 4 | | 2 4 0 0 2 4 4 0 2 | | 2 5 2 3 3 3 4 1 4 | | 4 0 2 0 2 4 2 4 0 | | 4 1 4 3 3 3 2 5 2 | | 4 3 2 1 3 5 4 3 2 | 9 9 o5 : Matrix ZZ <--- ZZ

To obtain all the information written by Normaliz set the option allComputations to true (to decide which information shall be written by Normaliz use the options for Normaliz, see setNmzOption). Then the method returns an object of type RationalCone whose keys are the suffixes of all the output files written, with value the content of the corresponding output file, which is an matrix whose rows contain the data computed, except for the suffix inv, for which the type is a HashTable (see also getNumInvs). It can also be used with the option grading.

 i6 : setNmzOption("allf",true); i7 : arc=normaliz(allComputations=>true,{(hy,"inequalities"),(eq,"equations"),(cg,"congruences")}); i8 : arc#"gen" o8 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 2 2 2 2 2 2 2 2 | | 2 3 4 5 3 1 2 3 4 | | 2 4 0 0 2 4 4 0 2 | | 2 5 2 3 3 3 4 1 4 | | 4 0 2 0 2 4 2 4 0 | | 4 1 4 3 3 3 2 5 2 | | 4 3 2 1 3 5 4 3 2 | 9 9 o8 : Matrix ZZ <--- ZZ i9 : arc#"ext" o9 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 4 0 0 2 4 4 0 2 | | 4 0 2 0 2 4 2 4 0 | 4 9 o9 : Matrix ZZ <--- ZZ i10 : arc#"inv" o10 = HashTable{class group => (1, 4, 4) } dim max subspace => 0 embedding dim => 9 external index => 4 graded => false hilbert basis elements => 9 inhomogeneous => false number extreme rays => 4 number support hyperplanes => 4 rank => 3 size triangulation => 2 sum dets => 8 o10 : HashTable