from the theory of proveit.linear_algebra.inner_products¶

see dependencies

In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import the special expression
from proveit.linear_algebra.inner_products import inner_prod_scalar_mult_right

In [2]:
# check that the built expression is the same as the stored expression
assert inner_prod_scalar_mult_right.expr == stored_expr
assert inner_prod_scalar_mult_right.expr._style_id == stored_expr._style_id
print("Passed sanity check: inner_prod_scalar_mult_right matches stored_expr")

Passed sanity check: inner_prod_scalar_mult_right matches stored_expr

In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{K}~\left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left[\forall_{a \in K}~\left[\forall_{x, y \in H}~\left(\left \langle x, a \cdot y\right \rangle = \left(a \cdot \left \langle x, y\right \rangle\right)\right)\right]\right]\right]

In [4]:
stored_expr.style_options()

Out[4]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()

Out[5]:
core typesub-expressionsexpression
0Operationoperator: 21
operand: 2
1ExprTuple2
2Lambdaparameter: 25
body: 3
3Operationoperator: 21
operand: 5
4ExprTuple5
5Lambdaparameter: 44
body: 7
6ExprTuple44
7Conditionalvalue: 8
condition: 9
8Operationoperator: 21
operand: 13
9Operationoperator: 11
operands: 12
10ExprTuple13
11Literal
12ExprTuple44, 14
13Lambdaparameter: 49
body: 16
14Operationoperator: 17
operand: 25
15ExprTuple49
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple25
19Operationoperator: 21
operand: 24
20Operationoperator: 40
operands: 23
21Literal
22ExprTuple24
23ExprTuple49, 25
24Lambdaparameters: 48
body: 26
25Variable
26Conditionalvalue: 27
condition: 28
27Operationoperator: 29
operands: 30
28Operationoperator: 31
operands: 32
29Literal
30ExprTuple33, 34
31Literal
32ExprTuple35, 36
33Operationoperator: 47
operands: 37
34Operationoperator: 45
operands: 38
35Operationoperator: 40
operands: 39
36Operationoperator: 40
operands: 41
37ExprTuple50, 42
38ExprTuple49, 43
39ExprTuple50, 44
40Literal
41ExprTuple51, 44
42Operationoperator: 45
operands: 46
43Operationoperator: 47
operands: 48
44Variable
45Literal
46ExprTuple49, 51
47Literal
48ExprTuple50, 51
49Variable
50Variable
51Variable