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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(ScalarMult(gamma, VecSum(index_or_indices = sub_expr1, summand = TensorProd(x, y, fi, z), domain = sub_expr2)), ScalarMult(gamma, TensorProd(x, 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(\gamma \cdot \left(\sum_{i=2}^{4} \left(x {\otimes} y {\otimes} f\left(i\right) {\otimes} z\right)\right)\right) = \left(\gamma \cdot \left(x {\otimes} y {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right) {\otimes} z\right)\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple9, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 16
operand: 13
9Variable
10Operationoperator: 20
operands: 12
11ExprTuple13
12ExprTuple23, 24, 14, 25
13Lambdaparameter: 32
body: 15
14Operationoperator: 16
operand: 19
15Conditionalvalue: 18
condition: 27
16Literal
17ExprTuple19
18Operationoperator: 20
operands: 21
19Lambdaparameter: 32
body: 22
20Literal
21ExprTuple23, 24, 26, 25
22Conditionalvalue: 26
condition: 27
23Variable
24Variable
25Variable
26Operationoperator: 28
operand: 32
27Operationoperator: 30
operands: 31
28Variable
29ExprTuple32
30Literal
31ExprTuple32, 33
32Variable
33Operationoperator: 34
operands: 35
34Literal
35ExprTuple36, 37
36Literal
37Literal