QyZBUS1IeXBlckludC5tcGw2IiEiIj5JOV9oeXBlcl9jaGVja19kaXZlcmdlbmNlc0dGJUkmZmFsc2VHJSpwcm90ZWN0ZWRHRiY= HyperInt, version 1.0, Copyright (C) 2014 Erik Panzer Please report any errors or suggestions to panzer@mathematik.hu-berlin.de Loading periods from /home/erikpanzer/HyperInt/Maple/periodLookups.m QyQ+SSVUZXN0RzYidCs2JCdJJWV4cHJHRiVJKGJvb2xlYW5HJSpwcm90ZWN0ZWRHPkkkbXNnR0YlUSFGJUYlRiVGJUAkNDkkWS1JJGNhdEdGKzYkUS5UZXN0fmZhaWxlZDp+RiU5JUYlRiVGJTYjIiIjISIi
<Text-field style="Heading 1" layout="Heading 1">Various simple graphs</Text-field>
<Text-field style="Heading 2" layout="Heading 2">One-loop vertex periods</Text-field> 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 [integrationStepsShuffle] took 0. seconds producing 1 terms [integrationStepsShuffle] took .8e-2 seconds producing 1 terms [integrationStepsShuffle] took .18e-1 seconds producing 1 terms [integrationStepsShuffle] took .24e-1 seconds producing 1 terms [integrationStepsShuffle] took .30e-1 seconds producing 1 terms [integrationStepsShuffle] took .38e-1 seconds producing 1 terms [integrationStepsShuffle] took .46e-1 seconds producing 1 terms [integrationStepsShuffle] took .57e-1 seconds producing 1 terms [integrationStepsShuffle] took .62e-1 seconds producing 1 terms [integrationStepsShuffle] took .71e-1 seconds producing 1 terms [integrationStepsShuffle] took .346 seconds producing 1 terms [integrationStepsShuffle] took .90e-1 seconds producing 1 terms [integrationStepsShuffle] took .98e-1 seconds producing 1 terms [integrationStepsShuffle] took .107 seconds producing 1 terms [integrationStepsShuffle] took .112 seconds producing 1 terms [integrationStepsShuffle] took .392 seconds producing 1 terms [integrationStepsShuffle] took .133 seconds producing 1 terms [integrationStepsShuffle] took .146 seconds producing 1 terms [integrationStepsShuffle] took .151 seconds producing 1 terms [integrationStepsShuffle] took .432 seconds producing 1 terms
<Text-field style="Heading 3" layout="Heading 3">Two-loop vertex in phi^3 theory</Text-field> QyQtSSVUZXN0RzYiNiMvLUkpaHlwZXJJbnRHRiU2JCokLCYqJiwmSSJhR0YlIiIiSSJBR0YlRjBGMCwqSSJiR0YlRjBJIkJHRiVGMEkiQ0dGJUYwSSJjR0YlRjBGMEYwKiYsJkYzRjBGNEYwRjAsJkY2RjBGNUYwRjBGMCEiJDcnRjVGNEYxRi9GNjcjNyQtSSIvRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJEYzIiIjNyIhIiI= Integrating variable C from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable C in .44e-1 seconds, produced 1 terms Integrating variable B from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable B in .25e-1 seconds, produced 3 terms Integrating variable A from 0 to infinity, integrand has 3 terms Warning, not checking divergences finished integration of variable A in .58e-1 seconds, produced 5 terms Integrating variable a from 0 to infinity, integrand has 5 terms Warning, not checking divergences finished integration of variable a in .67e-1 seconds, produced 4 terms Integrating variable c from 0 to infinity, integrand has 4 terms Warning, not checking divergences finished integration of variable c in .39e-1 seconds, produced 1 terms LUklVGVzdEc2IjYjLy1JKWh5cGVySW50R0YkNiQqKkkiYUdGJCIiIkkiYkdGJEYsSSJjR0YkRiwsKComRitGLEYtRixGLComRitGLEYuRixGLComRi1GLEYuRixGLCEiJDckRi5GLTcjNyQtSSIvRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJEYrIiIjNyI= Integrating variable c from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable c in .23e-1 seconds, produced 1 terms Integrating variable b from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable b in .21e-1 seconds, produced 1 terms
<Text-field style="Heading 2" layout="Heading 2">Dunce's cap</Text-field> LUklVGVzdEc2IjYkLy1JKWh5cGVySW50R0YkNiQtSSIqRyUqcHJvdGVjdGVkRzYkIyIiIiIiIywoKiQsJiomLCZJImFHRiRGL0kiYkdGJEYvRi8sJkkiY0dGJEYvSSJkR0YkRi9GL0YvKiZGOUYvRjpGL0YvISIjRi8qJCwmRjRGLyomRjZGL0Y3Ri9GL0Y8Ri8qJkY1RjxGOEY8ISIiNyVGOkY5Rjc3IzckKiRGNkZBNyJRLER1bmNlJ3N+Y2FwRiQ= Integrating variable d from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable d in .225 seconds, produced 1 terms Integrating variable c from 0 to infinity, integrand has 1 terms Warning, not checking divergences finished integration of variable c in .27e-1 seconds, produced 2 terms Integrating variable b from 0 to infinity, integrand has 2 terms Warning, not checking divergences finished integration of variable b in .25e-1 seconds, produced 1 terms
<Text-field style="Heading 2" layout="Heading 2">One-loop master integral / Euler's beta function</Text-field> QyQvLUklQmV0YUc2IjYkLCgiIiJGKUkieEdGJiEiIkkieUdGJkYpLCZGKUYpRixGKy1JJEludEdGJjYkKiYpSSJhR0YmLCRGLEYrRikpLCZGKUYpRjNGKSwmRipGKSEiI0YpRikvRjM7IiIhSSlpbmZpbml0eUclKnByb3RlY3RlZEdGKQ== Ly1JJUJldGFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwmIiIiRitJInlHRighIiIsKEYrRitJInhHRihGLUYsRistSSRJbnRHRiU2JComKUkiYUdGKCwkRixGLUYrKSwmRitGK0Y1RissJkYvRishIiNGK0YrL0Y1OyIiIUkpaW5maW5pdHlHRiY= Qyo+SSJORzYiIiM3ISIiPkkiWEdGJTciRic/KEkibkdGJSIiISIiIkYkSSV0cnVlRyUqcHJvdGVjdGVkRz8oSSJtR0YlRi1GLiwmRiRGLkYsRidGLz5GKTckLUkjb3BHRjA2I0YpNyQqLCksJEkieEdGJUYnRixGLiwmRi5GLkkiYUdGJUYuISIjLUkqZmFjdG9yaWFsR0YwNiNGLEYnKUkieUdGJUYyRi4tRkI2I0YyRic3JC1JIiRHRjA2JDcjLCZGP0YnRidGLkYsLUZKNiQ3IywkRj9GJ0YyRic+RiktSS9maWJyYXRpb25CYXNpc0dGJTYjLUkpaHlwZXJJbnRHRiU2JEYpRj9GJw== Integrating variable a from 0 to infinity, integrand has 91 terms Warning, not checking divergences finished integration of variable a in 14.987 seconds, produced 67 terms QyY+SSJCRzYiLUknc2VyaWVzRyUqcHJvdGVjdGVkRzYlLUklQmV0YUc2JEYoSShfc3lzbGliR0YlNiQsJiomSSJ0R0YlIiIiSSJ5R0YlRjIhIiJGMkYyLCgqJkYxRjJJInhHRiVGMkY0RjBGMkYyRjIvRjEiIiEsJkkiTkdGJUYyRjJGMkY0PkYkLUkkYWRkR0YoNiQtSSZjb2VmZkdGKDYlRiRGMUkibkdGJS9GQztGOUY7RjQ= 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 QyQtSSVUZXN0RzYiNiQvLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JJXN1YnNHRis2JDcjLUkkc2VxR0YrNiQvJkklemV0YUdGJTYjSSJuR0YlLUklWmV0YUdGKkY4L0Y5OyIiIyIjPywmSSJYR0YlIiIiSSJCR0YlISIiIiIhUS5CZXRhLWZ1bmN0aW9uRiVGRA==