Re: Inequalities into Standard Form

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Inequalities into Standard Form*From*: Edmund Greaves <egreaves>*Date*: Mon, 27 Jun 94 16:32:50 CDT

> > Some time ago, I wrote asking how to put > linear inequalities into standar form: > with all variable terms on the lhs, and > the constant term on the rhs. I wrote that > I could make such a function myself, but > hoped for something built-in or ready-made. > Eventually, I asked WRI tech support, and > am glad I did. Edmund Greaves, of WRI, > immediately started in on the problem, and > has sent me a far neater, and watertight, > function than anything I would have made. > Here is the function supplied by Ed Greaves > of Wolfram Research: > (I have to hand type everything, so any > mistakes are mine.) > > convertIneq[ x_[lhs_,rhs_] ] := > Module{temp,const,result}, > temp = Expand[ lhs - rhs ]; (*all terms to rhs*) > const = If[Head$ at {(J[temp] === Plus, > Select[temp, NumberQ], > 0]; > result = x[temp-const, -const]; > (* If a negative rhs is okay, done *) > (* If need rhs non-negative... *) > If[const>0, > result = Map[ Minus, result]; > result = result /. {Less -> Greater, > LessEqual->GreaterEqual, > Greater->Less, > GreaterEqual->LessEqual}]; > result > ] > > I hope this is of help to any one with similar problems. > > Ronald, I'm glad you found my solution useful. There was a slight typo in what you've given here so I thought I'd repost what I wrote: convertIneq[ x_[lhs_, rhs_] ] := Module[{temp, const, result}, temp = Expand[lhs - rhs]; (* move all terms to LHS *) const = If[Head[temp] === Plus, Select[temp, NumberQ], 0]; result = x[temp - const, -const]; If[const > 0, (* Is b negative on RHS? *) result = Map[Minus, result]; result = result /. {Less -> Greater, LessEqual -> GreaterEqual, Greater -> Less, GreaterEqual -> LessEqual}]; result ] Here are some examples of how you would use this function: In[2]:= convertIneq[2 (x - 1) == 1] Out[2]= 2 x == 3 In[3]:= convertIneq[-4 + 2 x + 3 y >= 1 - 4 x + 2 y] Out[3]= 6 x + y >= 5 In[4]:= ineq2 = x + y - 3 z - 1 <= 2 x - 5 Out[4]= -1 + x + y - 3 z <= -5 + 2 x In[5]:= convertIneq[ineq2] Out[5]= x - y + 3 z >= 4 The main use for this function is to convert inequalities to a form which could be used in a linear programming function. --------------------------------------------------------------------------- Edmund Greaves egreaves at wri.com {My views may or may not be the views of Wolfram Research} ---------------------------------------------------------------------------