# from the theory of proveit.linear_algebra.addition¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, V, a, b
from proveit.linear_algebra import InnerProd, Norm, VecAdd
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Exp, sqrt, two, zero

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two)))), And(InSet(a, V), InSet(b, V), Equals(InnerProd(a, b), zero)))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\right)} \textrm{ if } a \in V ,  b \in V ,  \left \langle a, b\right \rangle = 0\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 16
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10
6Operationoperator: 41
operand: 18
7Operationoperator: 35
operands: 12
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 16
operands: 17
11ExprTuple18
12ExprTuple19, 20
13ExprTuple43, 21
14Literal
15ExprTuple44, 21
16Literal
17ExprTuple22, 23
18Operationoperator: 24
operands: 30
19Operationoperator: 25
operands: 26
20Operationoperator: 27
operands: 28
21Variable
22Operationoperator: 29
operands: 30
23Literal
24Literal
25Literal
26ExprTuple31, 32
27Literal
28ExprTuple33, 39
29Literal
30ExprTuple43, 44
31Operationoperator: 35
operands: 34
32Operationoperator: 35
operands: 36
33Literal
34ExprTuple37, 39
35Literal
36ExprTuple38, 39
37Operationoperator: 41
operand: 43
38Operationoperator: 41
operand: 44
39Literal
40ExprTuple43
41Literal
42ExprTuple44
43Variable
44Variable