UpSet

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`UpSet`

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lhs^=rhs

assigns rhs to be the value of lhs, and associates the assignment with symbols that occur at level one in lhs.

Details

f[g[x]]=value makes an assignment associated with f. f[g[x]]^=value makes an assignment associated instead with g.
UpSet associates an assignment with all the distinct symbols that occur either directly as arguments of lhs, or as the heads of arguments of lhs.

Examples

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Basic Examples (1)Summary of the most common use cases

Define a symbolic property of a symbol:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-iftu28

Out[1]=1

Scope (2)Survey of the scope of standard use cases

^= defines upvalues:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-g0xwv

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0wgzeoz-8gjdi

Out[2]=2

If several symbols appear in the left-hand side, upvalues for all of them are defined:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-da10ki

In[2]:=2

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https://wolfram.com/xid/0wgzeoz-emo27v

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0wgzeoz-j7j950

Out[3]=3

Applications (1)Sample problems that can be solved with this function

Build a database of exchange rates:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-ecys0e

In[2]:=2

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https://wolfram.com/xid/0wgzeoz-kar0q

Out[2]=2

Properties & Relations (2)Properties of the function, and connections to other functions

^= defines upvalues in the same way as using a tag does:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-hd2hgj

In[2]:=2

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https://wolfram.com/xid/0wgzeoz-gfpi9

Out[2]=2

^= defines upvalues; = defines downvalues:

In[1]:=1

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https://wolfram.com/xid/0wgzeoz-cl9ax7

In[2]:=2

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https://wolfram.com/xid/0wgzeoz-djpt9m

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0wgzeoz-gi4pfi

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0wgzeoz-ouk3qv

Out[4]=4

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