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asked 2022-03-26 11:31:37 +0200

Cyrille gravatar image

Here is a code which works as expected

nl=3
nc=2
ring=QQ
A=matrix(ring,nl,nc,[3,2,1,4,1,1])
b=vector(ring,[3,5,6])
c=vector(ring,[4,7])
sign=list([">=",">=","<="])
vsign=list([">=",">="])
show(LatexExpr(r"\boldsymbol{A}="),A)
show(LatexExpr(r"\boldsymbol{b}="),b)
show(LatexExpr(r"\boldsymbol{c}="),c)
show(LatexExpr(r"\boldsymbol{Signs}="),sign)
show(LatexExpr(r"\boldsymbol{Vsigns}="),vsign)

def primal_lp(opt,A,b,c,signAb,signx):
    nc=A.ncols()
    x = var("x_", n=nc)
    X=[xj for xj in x]
    Zer1 =[0 for v in x]
    Zer2 =[0 for v in range(len(signAb))]
    con=A*vector(X)
    z=c*vector(X)
    from _operator import le, ge, eq
    op1=[ge  if v==">=" else (le if v=='<=' else eq)  for v in signx]
    tt1=list(map(lambda u,v:u(*v), op1 ,zip(X,Zer1)))
    op2=[ge  if v==">=" else (le if v=='<=' else eq)  for v in signAb]
    tt2=list(map(lambda u,v:u(*v), op1 ,zip(con,Zer2)))
    z1=flatten([opt,z,tt2,tt1])
    return show(z1)
    primal_lp('max',A,b,c,sign,vsign)

I would like to present the results like

$\max 4 x_0 + 7 x_1$

$3 x_0 + 2 x_1\geq 0 $

$x_0+4 x_1 \leq 0$

$x_0+x_1=0$

$x_0≥0$

$x_1≤0 $

I have tried to use table but I haven't found any way to obtain the desired representation. Any idea ?

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answered 2022-03-26 16:48:36 +0200

Emmanuel Charpentier gravatar image

updated 2022-03-27 22:03:30 +0200

One possible way to do it :

nl=3
nc=2
ring=QQ
A=matrix(ring,nl,nc,[3,2,1,4,1,1])
b=vector(ring,[3,5,6])
c=vector(ring,[4,7])
# Use expressions rather than strings : more useful, less hassle.
# sign=list([">=",">=","<="])
# vsign=list([">=",">="])
from _operator import eq, le, lt, ge, gt
# Don't scratch built-in "sign" function, it may come handy later on
hsign = [ge, ge, le]
vsign = [ge, ge]
# show(LatexExpr(r"\boldsymbol{A}="),A)
# show(LatexExpr(r"\boldsymbol{b}="),b)
# show(LatexExpr(r"\boldsymbol{c}="),c)
# show(LatexExpr(r"\boldsymbol{Signs}="),sign)
# show(LatexExpr(r"\boldsymbol{Vsigns}="),vsign)
# Neither Python's max nor Sage's symbolic_max accept a single argument,
# and neither denote maximization. Let's use an ad hoc symbolic function
maximize = function("maximize",
                    print_latex_func=lambda self, *args:
                    r"\text{maximize}\ %s"%latex(args[0]))

def primal_lp(opt,A,b,c,signAb,signx):
    nc=A.ncols()
    x = var("x_", n=nc)
    # X=[xj for xj in x] # This exact copy has no use.
    # X replaced by x afterwards...
    # Zer1 =[0 for v in x]
    Zer1 = [0]*len(x) # faster
    # Zer2 =[0 for v in range(len(signAb))]
    Zer2 = [0]*len(signAb) # MUCH faster
    con=A*vector(x)
    # z=c*vector(x) # Used once, put it inline...
    # from _operator import le, ge, eq # Done at toplevel
    # No neeed since we use expressions
    # op1=[ge  if v==">=" else (le if v=='<=' else eq)  for v in signx]
    tt1=list(map(lambda u,v:u(*v), signx ,zip(x,Zer1)))
    # Ditto
    # op2=[ge  if v==">=" else (le if v=='<=' else eq)  for v in signAb]
    tt2=list(map(lambda u,v:u(*v), signx ,zip(con,Zer2)))
    # z1=flatten([opt,z,tt2,tt1])
    # return show(z1)
    z1 = [opt(c*vector(x))]+tt2+tt1
    # If we want to return a table
    # z1=table([[u] for u in tt2+tt1],
    #          header_row=[opt(c*vector(x))])
    return z1

This returns a list of expressions :

sage: primal_lp(maximize,A,b,c,hsign,vsign)
[maximize(4*x_0 + 7*x_1),
 3*x_0 + 2*x_1 >= 0,
 x_0 + 4*x_1 >= 0,
 x_0 >= 0,
 x_1 >= 0]

whose tabulation is easy : view(table([[u] for u in primal_lp(maximize,A,b,c,hsign,vsign)])) will give you something like :

image description

[ I had to recourse to image conversion, since ask.sagemath.org's damn Mathjax won't accept tabular expressions :

sage: print(latex(table([[u] for u in primal_lp(maximize,A,b,c,hsign,vsign)])))
\begin{tabular}{l}
$\text{maximize}\ 4 \, x_{0} + 7 \, x_{1}$ \\
$3 \, x_{0} + 2 \, x_{1} \geq 0$ \\
$x_{0} + 4 \, x_{1} \geq 0$ \\
$x_{0} \geq 0$ \\
$x_{1} \geq 0$ \\
\end{tabular}

]

HTH,

EDIT : slelievre's suggestion worked (on Sagecell), and gave the following result :


\(\text{maximize}\ 4 \, x_{0} + 7 \, x_{1}\)
\(3 \, x_{0} + 2 \, x_{1} \geq 0\)
\(x_{0} + 4 \, x_{1} \geq 0\)
\(x_{0} \geq 0\)
\(x_{1} \geq 0\)

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Comments

I had to [resort] to image conversion [...]

Try html instead?

sage: p = primal_lp(maximize, A, b, c, hsign, vsign)
sage: t = table([[u] for u in p])
sage: print(html(t))
<div class="notruncate">
<table  class="table_form">
<tbody>
<tr class ="row-a">
<td style="text-align:left">\(\text{maximize}\ 4 \, x_{0} + 7 \, x_{1}\)</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">\(3 \, x_{0} + 2 \, x_{1} \geq 0\)</td>
</tr>
<tr class ="row-a">
<td style="text-align:left">\(x_{0} + 4 \, x_{1} \geq 0\)</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">\(x_{0} \geq 0\)</td>
</tr>
<tr class ="row-a">
<td style="text-align:left">\(x_{1} \geq 0\)</td>
</tr>
</tbody>
</table>
</div>
slelievre gravatar imageslelievre ( 2022-03-26 22:09:29 +0200 )edit

Which can be pasted into Ask Sage, and gets rendered as:


\(\text{maximize}\ 4 \, x_{0} + 7 \, x_{1}\)
\(3 \, x_{0} + 2 \, x_{1} \geq 0\)
\(x_{0} + 4 \, x_{1} \geq 0\)
\(x_{0} \geq 0\)
\(x_{1} \geq 0\)

slelievre gravatar imageslelievre ( 2022-03-26 22:10:36 +0200 )edit

Dear Samuel, your solution is clever for somebody who use a standard Latex distribution including Pdflatex. But I am working exclusively with Sagecell. I do not know if it is possible to call non pre installed packages of Sagemath. Nevertheless, I finally used some of your advices.

Cyrille gravatar imageCyrille ( 2022-03-27 20:04:27 +0200 )edit

Dear Cyrille, I was answering Emmanuel's complaint about having to include an image in his answer.

slelievre gravatar imageslelievre ( 2022-03-27 21:44:12 +0200 )edit

On websites rendering Markdown, MathJax is launched on expressions between dollar signs, so it is automatically in math mode. Not sure how to deal with a tabular then, especially a tabular with math expressions inside. But this is maybe getting off-topic here.

slelievre gravatar imageslelievre ( 2022-03-27 21:47:39 +0200 )edit

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Asked: 2022-03-26 11:31:37 +0200

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Last updated: Mar 27