Simulating the behaviour of Plus and Times.

• To: mathgroup at smc.vnet.net
• Subject: [mg75858] Simulating the behaviour of Plus and Times.
• From: Szabolcs <szhorvat at gmail.com>
• Date: Sat, 12 May 2007 03:03:17 -0400 (EDT)
• Organization: University of Bergen

```Is it possible to define two functions whose behaviour is the same as
that of Plus, Times and Minus in circumstances similar to the ones
illustrated below?

In[1]:= 1+2
Out[1]= 3

In[2]:= a + a
Out[2]= 2 a

In[3]:= 3a + 5a
Out[3]= 8 a

In[4]:= x a + y a
Out[4]= a x + a y

In[5]:= 3(a+b) + 2(a+b)
Out[5]= 5 (a+b)

In[6]:= 0a
Out[6]= 0

In[7]:= a-a
Out[7]= 0

Could someone show me how to define two such functions, plus and times,
that operate on integers represented as num[someNumber]? Example:

In := plus[times[num[2], plus[a, b]], times[plus[a, b], num[3]]]
Out = times[num[5], plus[a, b]]

In := plus[times[num[-1], a], a]
Out = num[0]

```

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