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Calling Sequence
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IsMinorOf(M1,M2)
IsMinorOf(M1,M2,mo,oo)
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Parameters
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M1
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Matroid
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M2
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Matroid
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mo
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(optional) equation of the form , where is a positive integer or the symbol
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oo
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(optional) equation of the form
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Description
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A matroid is a minor of another matroid if can be obtained from via a sequence of deletion and contraction operations. This procedure determines if is a minor of .
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In some cases, this question can be decided quickly, e.g., if has more entries in its ground set than , the answer is no. Otherwise, this command enters into a loop that can take quite a long time to run. By default, Maple will issue an error message if it computes that the loop may take more than iterations. To use a different limit for the current call, you can supply the option , where is either a positive integer or the symbol .
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By default, if is not a minor of , this command returns the value . If is indeed a minor of , it returns a sequence of three values: the constant and two subsets and of the ground set of such that is isomorphic to . The output can be modified using an option of the form .
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If you pass the option , the command returns just or .
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If you pass the option , the command returns just if is a minor of , and the symbol otherwise.
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If you pass the option , the command returns just if is a minor of , and the symbol otherwise.
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If you pass the option , where is a list consisting of any of the values , , and , the command returns an expression sequence of the corresponding outputs in the given order.
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If you pass the option , the command behaves as if the option had not been passed.
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Examples
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>
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Let us verify that the uniform matroid of rank 1 on 2 elements is a minor of the Fano matroid.
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We can verify the answer as follows.
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>
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References
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James G. Oxley. Matroid Theory (Oxford Graduate Texts in Mathematics). New York: Oxford University Press. 2006.
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