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Expression of type Equals

from the theory of proveit.linear_algebra.tensors

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import fi, gamma, i, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, four, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
expr = Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, TensorProd(y, fi)), domain = sub_expr2), z), TensorProd(x, ScalarMult(gamma, TensorProd(y, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), z))
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(x {\otimes} \left(\sum_{i=2}^{4} \left(\gamma \cdot \left(y {\otimes} f\left(i\right)\right)\right)\right) {\otimes} z\right) = \left(x {\otimes} \left(\gamma \cdot \left(y {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right)\right)\right) {\otimes} z\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 26
operands: 5
4Operationoperator: 26
operands: 6
5ExprTuple8, 7, 10
6ExprTuple8, 9, 10
7Operationoperator: 21
operand: 13
8Variable
9Operationoperator: 19
operands: 12
10Variable
11ExprTuple13
12ExprTuple23, 14
13Lambdaparameter: 36
body: 15
14Operationoperator: 26
operands: 16
15Conditionalvalue: 17
condition: 31
16ExprTuple29, 18
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operand: 25
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25
23Variable
24Operationoperator: 26
operands: 27
25Lambdaparameter: 36
body: 28
26Literal
27ExprTuple29, 30
28Conditionalvalue: 30
condition: 31
29Variable
30Operationoperator: 32
operand: 36
31Operationoperator: 34
operands: 35
32Variable
33ExprTuple36
34Literal
35ExprTuple36, 37
36Variable
37Operationoperator: 38
operands: 39
38Literal
39ExprTuple40, 41
40Literal
41Literal