Re: Kernel crashes in ReplaceAll - with or without Maximize failure

• To: mathgroup at smc.vnet.net
• Subject: [mg105241] Re: Kernel crashes in ReplaceAll - with or without Maximize failure
• From: dh <dh at metrohm.com>
• Date: Wed, 25 Nov 2009 02:33:46 -0500 (EST)
• References: <hedt65\$lnj\$1@smc.vnet.net>

DrMajorBob wrote:

> 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

>

Hi Bobby,

with version 7.0.1 on Vista, the following does not evaluate:

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

The parser seems to have problems with: x \[Element] Integers

It seems to work if one put this condition in an "Assuming":

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

Daniel

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