Re: FindInstance question? Any ideas to solve this equality.

• To: mathgroup at smc.vnet.net
• Subject: [mg128563] Re: FindInstance question? Any ideas to solve this equality.
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sun, 4 Nov 2012 00:44:22 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
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```On 11/2/12 at 11:51 PM, lrebanks at gmail.com (Lea Rebanks) wrote:

>FindInstance question:

>Hi All,

>I have evaluated the following equality with FindInstance function
>and there appears to be no results.

>Please could someone review the following equality to see if my
>result is TRUE or Is it possible to find one or more Integer results
>to this equality.

>radiusV1 = 145.98630072715727;
>radiusV2 = 95.62128455180272;
>slopeV1Deg = 9.462322208025617;
>slopeV2Deg = 18.43494882292201;

>FindInstance[(360*radiusV1)/(slopeV1Deg + 360*timeV1x) ==
>(360*radiusV2)/(slopeV2Deg + 360*timeV2x) &&
>(360*(radiusV1*2))/(slopeV1Deg*2 + 360*(timeV1x*2)) ==
>(360*(radiusV2*2))/(slopeV2Deg*2 + 360*(timeV2x*2)) &&
>timeV1x > 0 && timeV2x > 0, {timeV1x, timeV2x},
>Integers, 2]

>{}

It appears there are no integral solutions. That is I get the
same result as you even after replacing all machine precision
values with exact values and using other techniques.

Note, you do not accomplish anything by multiplying top/bottom
of one equation by a constant and adding this as a "new"
equation. Doing so, provides no additional information about
your variables. All that this can accomplish is make Mathematica
do more work.

Specifically,

In[1]:= eqns =
List @@ ((360*radiusV1)/(slopeV1Deg + 360*timeV1x) == (360*
radiusV2)/(slopeV2Deg +
360*timeV2x) && (360*(radiusV1*2))/(slopeV1Deg*2 +
360*(timeV1x*2)) == (360*(radiusV2*2))/(slopeV2Deg*2 +
360*(timeV2x*2)) && timeV1x > 0 && timeV2x > 0);

In[2]:= SameQ @@ Simplify[eqns[[;; 2]]]

Out[2]= True

So, your first two conditions are not linearly independent and
are really the same condition

```

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