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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, fi, gamma, 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 = [i]
sub_expr2 = ScalarMult(gamma, beta)
sub_expr3 = Interval(two, four)
sub_expr4 = TensorProd(x, fi, y)
expr = Equals(ScalarMult(sub_expr2, VecSum(index_or_indices = sub_expr1, summand = sub_expr4, domain = sub_expr3)), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, sub_expr4), domain = sub_expr3)).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(\left(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\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: 21
operands: 5
4Operationoperator: 9
operand: 8
5ExprTuple17, 7
6ExprTuple8
7Operationoperator: 9
operand: 12
8Lambdaparameter: 37
body: 11
9Literal
10ExprTuple12
11Conditionalvalue: 13
condition: 16
12Lambdaparameter: 37
body: 14
13Operationoperator: 21
operands: 15
14Conditionalvalue: 18
condition: 16
15ExprTuple17, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Operationoperator: 23
operands: 24
19Literal
20ExprTuple37, 25
21Literal
22ExprTuple26, 27
23Literal
24ExprTuple28, 29, 30
25Operationoperator: 31
operands: 32
26Variable
27Variable
28Variable
29Operationoperator: 33
operand: 37
30Variable
31Literal
32ExprTuple35, 36
33Variable
34ExprTuple37
35Literal
36Literal
37Variable