This Maple worksheet accompanies the paper [1]: Di Nardo E., G. Guarino, D. Senato (2011), A new algorithm for computing the multivariate Fa\303\240 di Bruno\342\200\231s formula, Applied Mathematics and Computation. doi:10.1016/j.amc.2011.01.001
A new algorithm for computing the
multivariate Fa\303\240 di Bruno\342\200\231s formula
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Di Nardo*
elvira.dinardo@unibas.it
http://www.unibas.it/utenti/dinardo/home.html;
Tel: +39 0971205890, Fax: +39 0971205896G. Guarino**
giuseppe.guarino@aspbasilicata.itD. Senato*
domenico.senato@unibas.it
* Dipartimento di Matematica e Informatica, Universit\303\240 degli Studi della Basilicata,
viale dell'Ateneo Lucano n.10, 85100 Potenza, Italy**Medical School, Universit\303\240 del Sacro Cuore (Rome branch),
Largo Agostino Gemelli n.8, 00168 Roma, ItalyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>Abstract: We provide a new algorithm for computing the multivariate Fa\303\240 di Bruno's formula. We follow a symbolic approach based on the classical umbral calculus that leads back the computation of the multivariate Fa\303\240 di Bruno's formula to a suitable multinomial expansion. The resulting computational times are faster compared with procedures existing in the literature.Application Areas/Subject: Combinatorics & algebraic methodsKeyword: multivariate composite function, Fa\303\240 di Bruno's formula, multivariate cumulants, multivariate Hermite polynomials, classical umbral calculus.See Also: background on the classical umbral calculus in [2], background on multiset subdivisions in [3], for different applications of multiset subdivisions see [5]
<Text-field style="Heading 1" layout="Heading 1">Initialization</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JFEocmVzdGFydEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIjtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGNi8lK2V4ZWN1dGFibGVHRjhGOQ==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
<Text-field style="Heading 1" layout="Heading 1">Subdivisions of a multiset</Text-field>This topic has been extensively discussed in [3]. See http://www.maplesoft.com/applications/view.aspx?SID=33039 for details.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
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Multivariate Fa\303\240 di Bruno\342\200\231s formula</Font></Text-field>A MAPLE algorithm for the computation of the multivariate Fa\303\240 di Bruno\342\200\231s formula by using the umbral equivalence (18) in [1].
<Text-field style="Heading 2" layout="Heading 2">Univariate and Multivariate Case</Text-field>MFB Functions
<Text-field style="Heading 3" layout="Heading 3">Introduction</Text-field>As we have proved in [3], the function makeTab generates a multiset subdivision (see the output of the function makeTab in the previous section). Parameters: 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 \342\210\210\342\204\225LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkNGLw==Univariate with UnivariateBy using the subdivisions of a multiset with all equal elements, we are able to compute the univariate Fa\303\240 di Bruno's formula, that is to expand LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkmbWZyYWNHRiQ2KC1GIzYmLUklbXN1cEdGJDYlLUkjbW9HRiQ2L1EwJkRpZmZlcmVudGlhbEQ7RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1JI21pR0YkNiVRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJy9GO1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnL0Y4USpbMCwwLDI1NV1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnRjotRiM2KC1GNDYtUSFGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUYjNidGMy1GMTYlLUZVNiVRInhGJ0ZYRmVuRlRGZ25Gam5GXG9GOkZhb0ZqbkZcb0Y6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgcC8lKWJldmVsbGVkR0ZCLUY0Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUZVNiVRImZGJ0ZYRmVuLUkobWZlbmNlZEdGJDYkLUYjNihGYW8tRiM2KC1GVTYlUSJnRidGWEZlbi1GNDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUZccTYkLUYjNiZGaG9Gam5GXG9GOkY6RmpuRlxvRjpGYW9Gam5GXG9GOkY6LUY0Ni5RIi5GJy9GXW9RJVRleHRGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUY0Ni5RIn5GJ0ZfckY6RkBGQ0ZFRkdGSUZLRk1GT0ZSRmpuRlxvRjo=For example in order to expand LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1GIzYkLUklbXN1cEdGJDYlLUkjbW9HRiQ2L1EwJkRpZmZlcmVudGlhbEQ7RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1GIzYkLUkjbW5HRiQ2JFEiMkYnRjpGOi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOi1GIzYmLUY0Ni1RIUYnRjpGQEZDRkVGR0ZJRktGTUZPRlItRiM2JUYzLUYxNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjtRJ2l0YWxpY0YnRlRGWkY6RmluRjovJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl5wLyUpYmV2ZWxsZWRHRkItRjQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjpGQEZDRkVGR0ZJRktGTUZPRlItRmFvNiVRImZGJ0Zkb0Znby1JKG1mZW5jZWRHRiQ2JC1GIzYmRmluLUYjNiYtRmFvNiVRImdGJ0Zkb0Znby1GNDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUZqcDYkLUYjNiRGYG9GOkY6RjpGaW5GOkY6Rjo= we call MFB(2) which gives 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 as output 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: the function MFB uses the function makeTab as we show in the following example. Calling makeTab(2) we have 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The first block 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 has two elements: its cardinality gives the index of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. The second block 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 has one element: its cardinality gives the index of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. The first element LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIxRidGMkYyLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= in the first block 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 has degree 1: its degree gives the index of LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1ElVGV4dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiVRIjFGJ0YyL0Y2USdub3JtYWxGJ0Y/LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=. Since in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiYtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSgmYWxwaGE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnRjpGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiLEYnRjovJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0YwRjpGOi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GRzYtUSFGJ0Y6RkovRk1GOUZPRlFGU0ZVRldGWS9GZ25GZW5GOg== we have two equal elements of degree 1, we get 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 This term must be multiplied with the integer (the multiplicity) that appears in each block (for example: 1 in 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 or n in 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). The second block 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 contains only one element with degree 2. This gives just 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 At the end, the summation of the two terms returns 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. Univariate with MultivariateWhen in the multiset there are two or more different elements, the result of a call to MFB is different from the previous one. For esample MFB(1,1) generates the following output: 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 that represents the expansion of 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. Indeed if in 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we replace 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: Similarly to what it happens for the univariate/univariate case, the function MFB calls the function makeTab as we show in the following example. Calling makeTab(1,1) we obtain 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 first block 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 has one element: its cardinality gives the index of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIi5GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlgtRkQ2LVEifkYnRj5GR0ZKRkxGTkZQRlJGVEZWRllGPg==The second block 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 has two elements: its cardinality gives the index of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. In the blocks, two variables 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 are involved. This explains why we use two indexes in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRImlGJ0YyRjUtSSNtb0dGJDYtUSIsRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYvNiVRImpGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGQQ== elements. In particular we have: 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 we have 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, and from the block LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiYtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSgmYWxwaGE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnRjpGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiLEYnRjovJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlRjMtRiM2JC1GQDYkUSIyRidGOkY6RkNGOkY6LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUZHNi1RIUYnRjpGSi9GTUY5Rk9GUUZTRlVGV0ZZL0ZnbkZlbkY6 we get 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. At the end, the summation of the two terms returns 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.
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field>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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>Univariate with Univariate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1GIzYkLUklbXN1cEdGJDYlLUkjbW9HRiQ2L1EwJkRpZmZlcmVudGlhbEQ7RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1JI21pR0YkNiVRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJy9GO1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjotRiM2Ji1GNDYtUSFGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUYjNiVGMy1GMTYlLUZVNiVRInhGJ0ZYRmVuRlRGZ25GOkZcb0Y6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcC8lKWJldmVsbGVkR0ZCLUY0Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUZVNiVRImZGJ0ZYRmVuLUkobWZlbmNlZEdGJDYkLUYjNiZGXG8tRiM2Ji1GVTYlUSJnRidGWEZlbi1GNDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y6RkBGQ0ZFRkdGSUZLRk1GT0ZSLUZncDYkLUYjNiRGY29GOkY6RjpGXG9GOkY6Rjo=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGSy8lKmxpbmVicmVha0dRJWF1dG9GJy1JI21pR0YkNiRRJE1GQkYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYjLUkjbW5HRiQ2JVEiMkYnLyUnaXRhbGljR0Y0Ri9GXW9GLy1GLDYuUSI7RidGXW9GL0YyL0Y2USV0cnVlRidGN0Y5RjtGPUY/RkEvRkVRLDAuMjc3Nzc3OGVtRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFEkTUZCRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiMtSSNtbkdGJDYlUSIzRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJ0Y7Rj4tSSNtb0dGJDYuUSI7RidGO0Y+LyUmZmVuY2VHRj0vJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=Univariate with Multivariate 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
<Text-field style="Heading 2" layout="Heading 2">The function <Font italic="true">joint</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">Introduction</Text-field>The procedure joint provides a way to multiply the factors of formula (22) in [1].Parameters: 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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmam9pbnRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GNjYmLUYjNiYtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRkIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGSi8lKnN5bW1ldHJpY0dGSi8lKGxhcmdlb3BHRkovJS5tb3ZhYmxlbGltaXRzR0ZKLyUnYWNjZW50R0ZKLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRj82JFEiMEYnRkJGQkZCLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkQtRjY2Ji1GIzYmRj5GREY+RkJGQkZqbkZdby1GRTYtUSFGJ0ZCRkgvRkxGSkZNRk9GUUZTRlVGVy9GZW5GWUZCRkJGQg==If we need to multiply MFB(1,0) with MFB(1,1) we must follow the following steps: 1) Call MFB(1,0) and 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 2) For each output, make the following evalutions: 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 where i=1..n. So from MFB(1,0) = 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, by using the previous evaluations, we have 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 From MFB(1,1) =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 3) Compute the following cefficients: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in the example 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 4) Multiply the two previous terms as follows: 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
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field>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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFEmam9pbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2JS1GMzYnLUYjNiUtSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GPDYlUSIwRidGP0ZCRj9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZELUYzNictRiM2JUY7RkRGO0Y/RkJGam5GXW9GP0ZCLUZFNi5RIjtGJ0Y/RkJGSEZKRk1GT0ZRRlNGVUZXL0ZlblEsMC4yNzc3Nzc4ZW1GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFEmam9pbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2JS1GMzYnLUYjNiUtSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Y7Rj9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZELUYzNictRiM2JS1GPDYlUSIyRidGP0ZCRkRGO0Y/RkJGZ25Gam5GP0ZCLUZFNi5RIjtGJ0Y/RkJGSEZKRk1GT0ZRRlNGVUZXL0ZlblEsMC4yNzc3Nzc4ZW1GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFEmam9pbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GMzYnLUYjNiUtSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GPDYlUSIwRidGP0ZCRj9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZELUYzNictRiM2JUY7RkRGO0Y/RkJGam5GXW9GRC1GMzYnLUYjNiVGZ25GREY7Rj9GQkZqbkZdb0Y/RkItRkU2LlEiO0YnRj9GQkZIRkpGTUZPRlFGU0ZVRlcvRmVuUSwwLjI3Nzc3NzhlbUYn
<Text-field style="Heading 2" layout="Heading 2">The function <Font italic="true">mkT</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">Introduction</Text-field>This procedure gives a list of all subvectors having the same lenght of a vector V and such that their summation returns V. Parameters: mkT(V, n), n\342\210\210\342\204\225Note: the output of 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: Suppose to call mkt([1,1],2).1) First the function makeTab is called: makeTab(1,1)=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) From this list and for each block, we consider only the first subblock, that is 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) Since the first block LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtb0dGJDYtUSFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSC1GIzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR0Y5RjQtRiM2JC1JI21uR0YkNiRRIjFGJ0Y0RjQvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GMTYtUTEmSW52aXNpYmxlVGltZXM7RidGNEY3RjpGPEY+RkBGQkZERkZGSS1GTjYlRlAtRiM2JC1GWTYkUSIyRidGNEY0RmZuRjRGMEY0RjQvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGMEY0 has cardinality one, we set 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 as we have asked for two blocks (that is two subvectors, note that the second parameter is n=2). So we have 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 [1,0],[0,1]4) The result is the list 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5) At the end, in order to have all lists, we need to permute the subblocks for each block, that is: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This function is used in the master function.
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field>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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>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
<Text-field style="Heading 2" layout="Heading 2">The Master Function <Font italic="true">UMFB</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">Introduction</Text-field>(Umbral Multivariate Fa`a di Bruno\342\200\231s Formula)All previous steps are combined in this procedure. The UMFB function recalls the MFB function for the univariate and the multivariate case (parameter n=1) and allows us to construct the multivariate-multivariate case (parameter n>1).Parameters: UMFB(V, n), V=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEkdGhlRicvJSdpdGFsaWNHRjRGL0YrLUZHNiVRJ291dHB1dEYnRkpGL0YrLUZHNiVRI2lzRidGSkYvRitGRkYrLUZHNiVRKmV4cGFuc2lvbkYnRkpGL0YrLUZHNiVRI29mRidGSkYvRi8=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: UMFB([1,3],2) = 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Pseudocode: UMFB(V, n)
if n = 1 then return( MFB(V) );
S := 0; for v in mkT( V, n ) do
S := S + joint(v) {with 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 } next for return(S); end:
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field>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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field>Univariate with Univariate 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 we have the same result of MFB function.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFElVU1GQkYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYzNictRiM2Iy1JI21uR0YkNiVRIjJGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnRj9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1JI21vR0YkNi5RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GPDYlUSIxRidGP0ZCRj9GQi1GSzYuUSI7RidGP0ZCRk5GUEZTRlVGV0ZZRmVuRmduL0Zbb1EsMC4yNzc3Nzc4ZW1GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JFElVU1GQkYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYzNictRiM2Iy1JI21uR0YkNiVRIjNGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnRj9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1JI21vR0YkNi5RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GPDYlUSIxRidGP0ZCRj9GQi1GSzYuUSI7RidGP0ZCRk5GUEZTRlVGV0ZZRmVuRmduL0Zbb1EsMC4yNzc3Nzc4ZW1GJw==Univariate with Multivariate 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Multivariate with Multivariate 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
<Text-field style="Heading 1" layout="Heading 1">Test Results</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Introduction</Text-field>In this section we analyze the accuracy of the results comparing the output obtained by using the Maple diff function (routine by which the multivariate Fa\303\240 di Bruno\342\200\231s formula is computable in Maple) .To this aim, we set: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 order to compare the results we have set up three functions: decoSub, deco and testUMFB.The decoSub function is an auxiliary routine useful for the deco function. The deco function takes the result of the function UMFB as input and gives an output equal to the Maple function diff. The testUMFB function checks the accuracy of the result.Parameter: 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where V, n are the same as the UMFB function and tDebug \342\210\210 {true, false} [set tDebug = true if you need to display also the output of the function diff]Example: 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We get the same result from 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;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<Text-field style="Heading 2" layout="Heading 2">The 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
<Text-field style="Heading 2" layout="Heading 2">Execution Samples</Text-field>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
<Text-field style="Heading 1" layout="Heading 1">Execution Time</Text-field>In this section we analize the difference of the execution time between the UMFB function and the Maple diff function.Notice: to perform an appropriate test, make a restart (using "!!!" for recall the entire worksheet) to clear any cash areas. 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
<Text-field style="Heading 1" layout="Heading 1">Conclusions</Text-field>By using the classical umbral calculus, we provide a new Maple algorithm for computing the multivariate Fa\303\240 di Bruno's formula for the following compositions: univariate with univariate, univariate with multivariate, multivariate with univariate, multivariate with the same multivariate, multivariate with different multivariates in any arbitrary number of components. The resulting algorithm is speeder of the routine MAPLE diff performing the same computations.
<Text-field style="Heading 1" layout="Heading 1">References</Text-field>[1] Di Nardo E., G. Guarino, D. Senato (2011), A new algorithm for computing the multivariate Fa\303\240 di Bruno\342\200\231s formula, Appl. Math. Comp. doi:10.1016/j.amc.2011.01.001 [2] Di Nardo, E., Senato, D. (2006) An umbral setting for cumulants and factorial moments. European J. Combin. 27, No. 3, 394\342\200\223413. (http://www.arxiv.org/abs/math/0412052)[3] Di Nardo E., G. Guarino, D. Senato, Multiset Subdivision, source Maple algorithm located in www.maplesoft.com (http://www.maplesoft.com/applications/view.aspx?SID=33039)[4] Di Nardo E., G. Guarino, D. Senato (2008) An unifying framework for k-statistics, polykays and their generalizations. Bernoulli. Vol. 14(2), 440-468. (http://www.unibas.it/utenti/dinardo/BEJ6163290408.pdf)
[5] Di Nardo E., G. Guarino, D. Senato, A Maple algorithm for k-statistics, polykays and their multivariate generalization, source Maple algorithm located in www.maplesoft.com (http://www.maplesoft.com/applications/view.aspx?SID=33040)Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities