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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 beta, i, x, y
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 = VecSum(index_or_indices = [i], summand = y, domain = Interval(two, four))
expr = Equals(ScalarMult(beta, TensorProd(x, ScalarMult(beta, sub_expr1))), ScalarMult(beta, ScalarMult(beta, TensorProd(x, sub_expr1))))
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(\beta \cdot \left(x {\otimes} \left(\beta \cdot \left(\sum_{i=2}^{4} y\right)\right)\right)\right) = \left(\beta \cdot \left(\beta \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} y\right)\right)\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: 13
operands: 5
4Operationoperator: 13
operands: 6
5ExprTuple17, 7
6ExprTuple17, 8
7Operationoperator: 15
operands: 9
8Operationoperator: 13
operands: 10
9ExprTuple18, 11
10ExprTuple17, 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 19
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Operationoperator: 20
operand: 22
20Literal
21ExprTuple22
22Lambdaparameter: 29
body: 24
23ExprTuple29
24Conditionalvalue: 25
condition: 26
25Variable
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Variable
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Literal