# 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 ExprTuple, V, a, b
from proveit.linear_algebra import InnerProd
from proveit.logic import Equals, InSet
from proveit.numbers import zero

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(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(a \in V, b \in V, \left \langle a, b\right \rangle = 0\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 5
operands: 4
2Operationoperator: 5
operands: 6
3Operationoperator: 7
operands: 8
4ExprTuple14, 9
5Literal
6ExprTuple15, 9
7Literal
8ExprTuple10, 11
9Variable
10Operationoperator: 12
operands: 13
11Literal
12Literal
13ExprTuple14, 15
14Variable
15Variable