# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Display multiplication and/or division of factors with the form x^y as one factor

Contributed by:
Ted Ersek

ResourceFunction["DisplayPowersTogether"][ displays the multiplication and/or division of factors with the form | |

ResourceFunction["DisplayPowersTogether"][ uses |

ResourceFunction["DisplayPowersTogether"] automatically combines factors at all levels of an expression.

Powers are displayed as one factor when valid under assuptions given by $Assumptions.

Combine the powers in an expression:

In[1]:= |

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Combine powers with multiple terms:

In[2]:= |

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Combine radicals:

In[3]:= |

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DisplayPowersTogether also combines products and quotients that include CubeRoot:

In[4]:= |

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DisplayPowersTogether combines exponents using the default assumptions stored in $Assumptions. The assumptions in this example are sufficient to combine all the exponents:

In[5]:= |

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DisplayPowersTogether similarly combines all the exponents when is given as a second argument in DisplayPowersTogether:

In[7]:= |

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Provide assumptions allowing some but not all exponents to be combined:

In[9]:= |

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Set $Assumptions as *a*>0, and specify *d*>0 as an assumption within DisplayPowersTogether:

In[10]:= |

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Only assume *d* > 0:

In[12]:= |

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The following assumptions are sufficient to combine all the exponents even though nothing is assumed about *b* or *z*:

In[14]:= |

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FullSimplify verifies that DisplayPowersTogether performed a valid transformation under the given assumptions:

In[15]:= |

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This performs independent verification by searching for a counterexample to the previous example. The identity is True in every case considered:

In[16]:= |

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In this case, nothing is assumed and none of the exponents can be combined:

In[17]:= |

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DisplayPowersTogether determines this can be done with a single Sqrt:

In[18]:= |

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Surd is a generalization of CubeRoot. DisplayPowersTogether combines expressions involving Surd when appropriate:

In[19]:= |

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In[20]:= |

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Rather than use $Assumptions or DisplayPowersTogether[*expr*,*assum*], assumptions can be provided using Assuming:

In[21]:= |

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Two examples are given here where Simplify can combine a sum of terms:

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DisplayPowersTogether does not handle sums or differences:

In[24]:= |

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In[25]:= |

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The result of DisplayPowersTogether has a Head of Defer:

In[26]:= |

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In[27]:= |

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It is not a readily-computable expression:

In[28]:= |

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First can be used to compute on the results:

In[29]:= |

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Alternatively, copy the output shown previously and evaluate it to perform the computation:

In[30]:= |

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DisplayPowersTogether can be used again to ensure the square roots are combined again:

In[31]:= |

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The next example is not in a form that allows DisplayPowersTogether to combine factors:

In[32]:= |

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When the cube root above is distributed across the sum, DisplayPowersTogether can combine factors:

In[33]:= |

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- Power–Wolfram Mathematical Functions Site
- Sqrt–Wolfram Mathematical Functions Site
- A Function Called HoldTemporary–Wolfram Library Archive
- Force Maximum Simplification of Radicals in a Traditional Way-How to do it?–Mathematica Stack Exchange

- 1.0.0 – 02 October 2020

This work is licensed under a Creative Commons Attribution 4.0 International License