** Using WeBWorK **

1x+0y+7z=8.

Is there an easy way to write the code so that the "1x" is just "x" and the "0y" doesn't appear? We've already considered creating the correct output string using many if, then statements, but that gets very complicated for a 3 x3 or 4 x 5 system.

-Tom

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sub Mat2System{
    my $coeffs=shift();
    my $vec = shift();
    my ($srow,$scol) = $coeffs->dim();
    my ($vrow,$vcol) = $vec->dim();
    die "Wrong number of rows or columns" if (($vcol !=1) || ($vrow != $srow));
    my $outstr="\begin{matrix}";
    my $s;

for(my $j=0;$j<$srow;$j++){
$s=0;
for(my $i=0,my $vn=1;$i<$scol;$i++,$vn++){
my $a=$coeffs->element($j+1,$i+1);
if($a==0){
$outstr = $outstr . '&&';
}elsif($a>0){
if($a==1){$a="";}
if($s==0){$outstr = $outstr . "& $a x_{$vn}";$s=1;}
else{$outstr=$outstr . "&+& $a x_{$vn}";}
}else{
if($s == 1){
$a=-$a;
if($a==1){$a="";}
$outstr= $outstr . "&- &$a x_{$vn}";
}else{$outstr = $outstr . "& $a x_{$vn}";$s=1;}
}
}
$outstr = $outstr . "&=&" . $vec->element($j+1,1). "\\";
}
$outstr= $outstr . 'end{matrix}';
return $outstr;
}

Example of use:

$A1=Matrix->new_from_array_ref( [[2,-1],[0,3]]);
$solution1=[-2,3];  #What do we want the solution to be?
$x1=Matrix->new_from_array_ref([$solution1]);
$x1 = ~$x1; #transpose
$b1 = $A1*$x1;
$C1=Mat2System($A1,$b1);

BEGIN_TEXT
Solve the following system by back substitution:
[ $C1 ]
END_TEXT

It shouldn't be too hard to modify it to take a list of variable names as an extra argument or use a different list of variable names. I'm revising some problems now. I may try modifying this to use the Parser's matrices.

Bob

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If you want a system of equations with the x,y,... columns lined up, you may need something like what is above. If you have a single equation, you can use nicestring which is in webwork (in PGbasicmacros). You can get a string version of $a x + $b y + $c z + $d with

$polystring = nicestring([$a, $b, $c, $d],['x', 'y', 'z', '']);

If you are setting up a system, then you can use this to produce left-hand sides and align on the equal signs, which would produce output like

2x + 3y - z = 5
    4x + 5z = -7
     -y + z = 0

John

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    loadMacros("Parser.pl");

Context()->variables->are(x=>'Real',y=>'Real',z=>'Real');
$f = Formula("1x+0y+7z")=>reduce;

BEGIN_TEXT
\(f(x,y,z) = \{$f->TeX\}\)
END_TEXT

would produce "f(x,y,z) = x + 7z" as its output.

You can include equalities in your formulas if you enable the equality operator (which is not enabled by default):

    Parser::BOP::equality::Allow();

Then you can do things like

    $f = Formula("1x+0y+7z=8")->reduce;

Some of the reduction rules may not be appropriate for what you are doing, but they can be turned on and off in the context. If you want to do that, let me know (it is not well documented, as is the case for most of the parser at the moment).

There is basic documentation on how to use the parser in ww2/doc/parser/docs. There still needs to be a lot more, but it is a start.

Davide

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Davide

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$a=random(-1,1,2);

$b=-1;

$ex="$a x + $b";$ex=~s/\+ -/- /s;$ex=~s/1 x /x /s;

Above code simply substitutes any

-1 x with -x,

1 x with x,

+ - with -

so an expression like \( $ex \) looks nice on the screen.

Lars.

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It will also convert 11 x to 1 x. I realize your values for $a don't go that high, but if someone tries to use this approach elsewhere, they could get caught by this. That is one of the hidden "gotchas" in using pattern matching rather than symantic analysis for doing this kind of thing.

Davide

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Thanks, Tom

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$A1=Matrix->new_from_array_ref( [[2,-1],[0,3]]); $solution1=[-2,3]; #What do we want the solution to be? $x1=Matrix->new_from_array_ref([$solution1]); $x1 = ~$x1; #transpose $b1 = $A1*$x1; $variablenames=Matrix->new_from_array_ref( [['x'],['y']] ); $C1=Mat2System($A1,$b1,$variablenames);

BEGIN_TEXT Solve the following system by back substitution: ( $C1 ) END_TEXT

sub Mat2System{ my $coeffs=shift(); my $vec = shift(); my $vname=shift(); my ($srow,$scol) = $coeffs->dim(); my ($vrow,$vcol) = $vec->dim(); my ($vnamerow,$vnamecol) = $vname->dim(); die "Wrong number of rows or columns" if (($vcol !=1) || ($vrow != $srow) || ($vnamecol !=1) || ($vrow != $vnamerow)); my $outstr="\begin{array}"; my $s;

$outstr = $outstr . '{r'; for(my $j=0; $j<$scol; $j++){ $outstr = $outstr . 'rr'; } $outstr = $outstr . 'r}';

for(my $j=0;$j<$srow;$j++){ $s=0; for(my $i=0,my $vn=1;$i<$scol;$i++,$vn++){ my $varname=$vname->element($vn,1); my $a=$coeffs->element($j+1,$i+1); if($a==0){ ## if coefficient is 0 then goto the next column by putting 2 &&'s $outstr = $outstr . '&&'; }elsif($a>0){ if($a==1){$a="";} if($s==0){$outstr = $outstr . "& $a \,$varname";$s=1; } else{$outstr=$outstr . "&+& $a \, $varname";} }else{ if($s == 1){ $a=-$a; if($a==1){$a="";} $outstr= $outstr . "&- &$a \,$varname"; }else{$outstr = $outstr . "& $a \, $varname";$s=1;} } } $outstr = $outstr . "&=&" . $vec->element($j+1,1). "\\"; } $outstr= $outstr . ' end{array}'; return $outstr; }

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