Re: Bug in RowReduce of a matrix with symbolic entries

• To: mathgroup at smc.vnet.net
• Subject: [mg70798] Re: Bug in RowReduce of a matrix with symbolic entries
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Sat, 28 Oct 2006 05:21:32 -0400 (EDT)
• References: <ehs2cs\$o5b\$1@smc.vnet.net>

```RowReduce can treat matrix with symbolic entries
A simple example

Trace[RowReduce[{{3, 1, a}, {2, 1, b}}], TraceInternal -> True]
{HoldForm[RowReduce[{{3, 1, a}, {2, 1, b}}]], {{HoldForm[1/3],
HoldForm[1/3]}, HoldForm[a/3], HoldForm[a/3]},
{HoldForm[Expand[a/3]], HoldForm[a/3]}, {HoldForm[Together[-2*a +
3*b, Trig -> True]], HoldForm[-2*a + 3*b]},
{HoldForm[Expand[a/3 + (1/3)*(2*a - 3*b)]], HoldForm[a - b]},
{HoldForm[Together[a - b, Trig -> True]], HoldForm[a - b]},
HoldForm[{{1, 0, a - b}, {0, 1, -2*a + 3*b}}]}

Information[TraceInternal]
"TraceInternal is an option for Trace and related functions which, if
True or False, specifies whether to trace evaluations of \
expressions generated internally by Mathematica. The intermediate
Automatic setting traces a selected set of internal \
evaluations including Messages and sets or unsets of visible symbols."
Attributes[TraceInternal] = {Protected}

Howver, your matrix causes problem to TowReduce as it can be seen by
the following
command

Trace[RowReduce[{{1, 1, 1, p}, {-2, -1, -1, q}, {-3, -3, -2, r}, {0, 2,
2, s}, {-2, -4, -5, t}}], TraceInternal -> True]
{HoldForm[RowReduce[{{1, 1, 1, p}, {-2, -1, -1, q}, {-3, -3, -2, r},
{0, 2, 2, s}, {-2, -4, -5, t}}]],
{HoldForm[Expand[2*(2*p + q) - s]], HoldForm[4*p + 2*q - s]},
{{HoldForm[1/2], HoldForm[1/2]}, HoldForm[s/2], HoldForm[s/2]},
{HoldForm[Expand[s/2]], HoldForm[s/2]}, {HoldForm[Expand[0]],
HoldForm[0]}, {HoldForm[Expand[0]], HoldForm[0]},
{HoldForm[Expand[0]], HoldForm[0]}, {HoldForm[Expand[0]],
HoldForm[0]},
HoldForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0,
0, 0, 0}}]}

Regards
Dimitris

```

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