I have the following code for determiningsimplifying an inequality using Simplify[], the codes are as follows:
glbcond=glbcond =
{0 < d1 < 1, d1 \[Element]∈ Reals, 0 < d2 < 1, d2 \[Element]∈ Reals,
0 < d3 < 1, d3 \[Element]∈ Reals, 0 < e1 < 1, e1 \[Element]∈ Reals,
0 < e2 < 1, e2 \[Element]∈ Reals, 0 < e3 < 1, e3 \[Element]∈ Reals,
0 < Hd < 1, Hd \[Element]∈ Reals, 0 < Hu < 1, Hu \[Element]∈ Reals,
0 < L1 < 1, L1 \[Element]∈ Reals, 0 < L2 < 1, L2 \[Element]∈ Reals,
0 < L3 < 1, L3 \[Element]∈ Reals, 0 < Q1 < 1, Q1 \[Element]∈ Reals,
0 < Q2 < 1, Q2 \[Element]∈ Reals, 0 < Q3 < 1, Q3 \[Element]∈ Reals,
0 < u1 < 1, u1 \[Element]∈ Reals, 0 < u2 < 1, u2 \[Element]∈ Reals,
0 < u3 < 1, u3 \[Element]∈ Reals};
z2cond=Hdz2cond =
Hd < Hu < L1 < L2 < L3 < Q1 < Q2 < Q3 < u1 < u2 < u3 < d1 < d2 < d3;
In[97]:=Simplify[Abs Simplify[Abs@@ (Q1 u1)/(d2 Q3)<1 < 1, (And@@glbcond)&&z2cond]
Out[97]=And Q1@@ u1<d2glbcond) Q3&& z2cond]
Q1 u1 < d2 Q3
However, if I turn up the SystemOptions
as suggested by this related post [here][1]here as
SetSystemOptions["SimplificationOptions"SetSystemOptions[
"SimplificationOptions" -> "AssumptionsMaxNonlinearVariables" -> 14]
I get
In[99]:= Simplify[Abs[(Q1 u1)/(d2 Q3)]<1] < 1,glbcond&&z2cond]
Out[99]= Trueglbcond && z2cond]
True
So my question is, how exactly are the numbers of non-linear variables calculated? As far as I can see from my example, all the inequalities inside the argument for assumption are linear. Or fordoes the calculation of number of non-linear variables involvesinvolve both of the two arguments sitting inside of Simplify[]Simplify
?
This my first post in MMA stackexchange, hopeon Mathematica.SE. I hadhope my post meets the right syntax andsite's posting conventions :) [1]: Checking inequalities: How can $x>0,y>0$ yet $x+y$ indeterminate?