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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, i, u, v, w, x, z
from proveit.linear_algebra import TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, five, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(one, five)
expr = Equals(TensorProd(u, v, w, x, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2), z), VecSum(index_or_indices = sub_expr1, summand = TensorProd(u, v, w, x, fi, z), domain = sub_expr2)).with_wrapping_at(1)
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())
\begin{array}{c} \begin{array}{l} \left(u {\otimes} v {\otimes} w {\otimes} x {\otimes} \left(\sum_{i=1}^{5} f\left(i\right)\right) {\otimes} z\right) \\  = \left(\sum_{i=1}^{5} \left(u {\otimes} v {\otimes} w {\otimes} x {\otimes} f\left(i\right) {\otimes} z\right)\right) \end{array} \end{array}
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.()(1)('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: 15
operands: 5
4Operationoperator: 9
operand: 8
5ExprTuple18, 19, 20, 21, 7, 23
6ExprTuple8
7Operationoperator: 9
operand: 12
8Lambdaparameter: 29
body: 11
9Literal
10ExprTuple12
11Conditionalvalue: 13
condition: 17
12Lambdaparameter: 29
body: 14
13Operationoperator: 15
operands: 16
14Conditionalvalue: 22
condition: 17
15Literal
16ExprTuple18, 19, 20, 21, 22, 23
17Operationoperator: 24
operands: 25
18Variable
19Variable
20Variable
21Variable
22Operationoperator: 26
operand: 29
23Variable
24Literal
25ExprTuple29, 28
26Variable
27ExprTuple29
28Operationoperator: 30
operands: 31
29Variable
30Literal
31ExprTuple32, 33
32Literal
33Literal