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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 a, u, v, w, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.logic import Equals
In [2]:
# build up the expression from sub-expressions
sub_expr1 = ScalarMult(a, v)
expr = Equals(TensorProd(u, sub_expr1, VecAdd(w, x, y), z), VecAdd(TensorProd(u, sub_expr1, w, z), TensorProd(u, sub_expr1, x, z), TensorProd(u, sub_expr1, y, 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(u {\otimes} \left(a \cdot v\right) {\otimes} \left(w + x + y\right) {\otimes} z\right) = \left(\left(u {\otimes} \left(a \cdot v\right) {\otimes} w {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} x {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} y {\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: 15
operands: 5
4Operationoperator: 11
operands: 6
5ExprTuple19, 20, 7, 22
6ExprTuple8, 9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 15
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 18, 21
13ExprTuple19, 20, 17, 22
14ExprTuple19, 20, 18, 22
15Literal
16ExprTuple19, 20, 21, 22
17Variable
18Variable
19Variable
20Operationoperator: 23
operands: 24
21Variable
22Variable
23Literal
24ExprTuple25, 26
25Variable
26Variable