Kernel crashes in ReplaceAll - with or without Maximize failure

• To: mathgroup at smc.vnet.net
• Subject: [mg105181] Kernel crashes in ReplaceAll - with or without Maximize failure
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Mon, 23 Nov 2009 06:54:09 -0500 (EST)

```Two years ago this worked properly, with the output shown:

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]
Maximize[{proxy, x \[Element] Integers, x <= 20}, x]
eq /. Last@%

1.96128*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/509872338168900 + (10 x)/3 - (3 x^2)/10 + x^3/150

{5567805932804389/509872338168900, {x -> 7}}

10.92

Today the same code outputs a Maximize failure and crashes the kernel:

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]
Maximize[{proxy, x \[Element] Integers, x <= 20}, x]
eq /. Last@%

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150

Maximize[{1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150, x \[Element] Integers, x <= 20}, x]

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3 /. x

Ditto with this code (moving Integers to the third argument):

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]
Maximize[{proxy, x <= 20}, x, Integers]
eq /. Last@%

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150

Maximize[{1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150, x <= 20}, x, Integers]

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3 /. Integers

Odder yet, the kernel doesn't crash in Fit, Rationalize, or even Maximize,
but rather, in ReplaceAll (which does nothing), yet AFTER the FE outputs a
result:

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150

Maximize[{proxy, x <= 20}, x, Integers]

Maximize[{1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150, x <= 20}, x, Integers]

eq /. Last@%

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3 /. Integers

Same here, without LessEqual:

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]
Maximize[proxy, x, Integers]

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150

Maximize[1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150, x, Integers]

eq /. Last@%

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3 /. Integers

And same here, after outputting a correct result:

data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
eq = Fit[data, {1, x, x^2, x^3}, x]
proxy = Rationalize[eq, 10^-15]
Maximize[proxy, x]

2.63678*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3

1/379250494936462 + (105718301111983 x)/31715490333595 - (
3 x^2)/10 + x^3/150

{\[Infinity], {x -> \[Infinity]}}

{\$Version, \$ReleaseNumber}

{"7.0 for Mac OS X x86 (64-bit) (February 19, 2009)", 1}

What's going on????

Bobby

--
DrMajorBob at yahoo.com

```

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